The poet of the Roll of Arms of Caerlaverock in 1300 - the man who waxed lyrical about the wonders of Lord Clifford - said this about Richard Fitzalan: "Richard, the earl of Arundel/A handsome and well-loved knight/I saw there richly armed/In red, with a gold lion rampant." (Richart le conte de Arondel/Beau chevalier et bien amé/ I vi-je richement armé/En rouge, au lyon rampant de or).  Richard's arms can be seen here. An interesting fact about him: he was twice excommunicated (and absolved) by Gilbert de St Leofard, bishop of Chichester, for hunting without permission in the bishop's woods.  You'd think Richard might have learnt his lesson the first time, especially as he had to make a humiliating submission to Gilbert in order to gain absolution.
Earl Richard: What shall we do today? I know! Let's go hunting in the bishop of Chichester's woods!
Earl Richard's servant: Ummm, I'm not sure that's such a good idea, my lord. Remember what happened the last time.
Earl Richard: The excommunication, you mean? Oh, that was just a silly misunderstanding. I'm sure the bishop won't mind this time.
Although the date of Richard's death is often given, even in the Oxford Dictionary of National Biography and the Complete Peerage, as 9 March 1302, he in fact died a little earlier than that, shortly before 15 January 1302, on which date the escheator was ordered to take his lands into the king's hand. An entry on the Close Roll of 2 February 1302 confirms that Richard was already dead then: he owed Edward I £1000, and the king sent his serjeant William Persone to select the "better and more beautiful horses" from Richard's stud-farms in Clun and Oswestry in part payment of the debt.  Richard was buried next to his wife, who died in 1292 in her early or mid-twenties, at Haughmond Abbey near Shrewsbury, burial place of many of the Fitzalans. He was the last of his family in the Middle Ages to use the name Fitzalan on a regular basis, and his descendants in the fourteenth and fifteenth centuries usually just called themselves Arundel or de Arundel.
Eleanor (Alianore), Lady Percy
It is not completely 100% certain that Eleanor Percy was Earl Richard's daughter as no contemporary source connects the two beyond doubt, although the Alnwick chronicle and a genealogy of the Percy family in the Whitby Chartulary (see here) name Eleanor as a daughter of the earl of Arundel, which can only mean Richard. Some websites say that Eleanor was the daughter of John Fitzalan and Isabella Mortimer and thus Richard's sister, but as John Fitzalan was never earl of Arundel, this doesn't fit. Eleanor Percy was certainly born an Arundel, Edward II acknowledged her as 'the king's kinswoman' on numerous occasions,  and the fact that she married Lord Percy is indirect proof that she was of high rank and therefore most likely to be the earl's daughter, not from a cadet branch of the family. Assuming that Alesia di Saluzzo was Eleanor's mother, Eleanor and Edward II were third cousins once removed via common descent from the counts of Savoy; without the Saluzzo connection you have to go all the way back to the eleventh century to find a common ancestor. Richard, earl of Arundel acknowledged a debt of 2000 marks to Henry Percy in August 1300, presumably Eleanor's dowry (Richard paid the same amount to Bishop Robert Burnell for his sister Maud's marriage to the bishop's nephew Philip in 1283), and Henry Percy acknowledged in November 1313 that he had received full payment of all debts from Richard's son and heir Edmund. 
Eleanor's husband Henry, Lord Percy was born around 25 March 1273 as the posthumous son of Henry Percy - the family was not imaginative with names - and through his mother was the grandson of John de Warenne, earl of Surrey (1231-1304). Given that Eleanor and Henry's first child, another Henry who married Idonea Clifford, was born in February 1301, this probably means that Eleanor was the eldest child of Earl Richard and Alesia, older than her brother Earl Edmund (born 1 May 1285) and born about 1283 or 1284. If she was born before her brother, Earl Richard can only have been sixteen or seventeen at the time, but his grandfather Roger Mortimer (died 1282) and first cousin Roger Mortimer (died 1330) also became fathers at the age of about sixteen. I wonder if Eleanor was named after Queen Eleanor of Castile or Queen Eleanor of Provence, as it wasn't a name used in either of her parents' families. If Eleanor married Henry Percy in or shortly before 1300, as the debt from Earl Richard to Percy indicates, it makes far more sense that she was born in the 1280s rather than 1272, which is the latest she can have been born if she was Earl Richard's sister (as his father John Fitzalan died in March 1272). It would have been extremely unusual for a noblewoman to marry in her late twenties.
EDIT: Thank you to Paul Martin Remfry for kindly providing me with information from the Wigmore Chronicle, which states in 1287 that "The same year about 29 June, a daughter named Eleanor was born to Richard of Arundel." This means that Eleanor was a little more than two years younger than her brother Earl Edmund and considerably younger than her husband, and still only fourteen when her son Henry was born in February 1301. She must have become pregnant very soon after marriage.
Although Henry Percy started Edward II's reign as a household knight and trusted ally of the king, Edward's favouritism towards Piers Gaveston pushed him into opposition, and Henry was one of the men who besieged Piers in Scarborough Castle in May 1312 with, among others, his first cousin the earl of Surrey. The king had on 28 January 1312, shortly after Piers' return to England, rescinded his appointment of Henry as constable of Bamburgh and told the former constable, Lady Vescy, to retain possession, "the king being unwilling that Henry de Percy, to whom he has granted it, should have the custody thereof." Edward replaced Henry as constable of Scarborough Castle at the same time.  The king ordered Henry's arrest and seized his lands at the end of July 1312, on the grounds that "upon the surrender of Pieres de Gavaston, earl of Cornwall, at Scardeburgh, [Henry] had gone security for his safety until a certain date, and had not surrendered when the earl was put to death before that time."  Not suprisingly Henry declined to fight for Edward at Bannockburn in June 1314, and died shortly before 10 October that year at the age of forty-one, leaving his thirteen-year-old son Henry as his heir.  He was buried at Fountains Abbey.
Despite her husband's difficulties with the king, Eleanor Percy herself was on good terms with Edward II, who often acknowledged her as his kinswoman, granted favours at her request and appointed her constable of Scarborough Castle in November 1325 (she was re-appointed in February 1327 at the beginning of Edward III's reign). Eleanor was dead by 13 August 1328, when an entry on the Fine Roll mentions her executors and that her son had been appointed constable of Scarborough. 
Edmund, earl of Arundel
Born on 1 May 1285 when his father was eighteen and his mother probably younger, married Alice de Warenne, sister of the earl of Surrey and first cousin of his sister's husband Henry Percy, in about 1305 and had children, including his heir Richard, earl of Arundel (c. 1313-1376). Edmund was beheaded with Robert de Micheldever and John Daniel on the orders of his cousin Roger Mortimer in Hereford on 17 November 1326, without a trial and attainted posthumously, because of Mortimer's "perfect hatred" of him. (Mortimer and Isabella demonstrating how their regime would be so much fairer and less tyrannical and capricious than Edward II and Hugh Despenser's.)
Sir Richard de Arundel
Sir Richard was certainly the brother of Eleanor Percy, who was the executor of his will and named as his sister on several occasions, and therefore almost certainly a son of Earl Richard and Countess Alesia, even though nothing definitively connects them. Richard was acknowledged as Edward II's kinsman in at least one writ and was his 'bachelor', or household knight. The Italian banking firm the Ballardi of Lucca acknowledged in June 1311 that they owed Richard 400 marks, and Edward granted him four manors in four counties in April 1314 to provide him with an income of eighty pounds a year. Richard was captured at Bannockburn in June 1314, whereupon Edward II, declaring himself desirous "to hasten his delivery from the hands of the Scots," appointed keepers of Richard's lands and told them to keep his goods safe for his eventual return. Richard was dead by 24 November 1314, whether still in captivity in Scotland or back in England, I'm not sure. I haven't found a mention of any children, and his manors were taken back into the king's hand. His sister Eleanor Percy was repairing the bridge at Wetherby in 1316 "for the good of the soul of the said Richard." 
Master John de Arundel
The second or third son of Earl Richard and Countess Alesia and probably born in 1290, as a letter of Pope Clement V says that he was fifteen and "having only the first tonsure" in January 1306.  Numerous other papal letters and entries in the chancery rolls confirm that John - presumably named after his grandfather John Fitzalan, lord of Clun and Oswestry - was Earl Richard's son. He held degrees in canon and civil law and was a papal chaplain, canon of Lincoln, Lichfield, York and Chichester, warden of the royal chapel of Tickhill, rector of Bury, Arncliffe and Westbourne, and so on. One of Pope John XXII's letters says that John was appointed canon of Lincoln in 1320 at the request of his kinsmen Edward II and Philip V of France (John's fourth cousin) and their queens. Edward II acknowledged John as 'cousin' on occasion, and in August 1310, sent him to the Curia with Boniface and George of Saluzzo, John's uncles (Alesia's brothers) and fellow clerics, whom Edward II also often acknowledged as his relatives. 
The Oxford Dictionary of National Biography says that John was still alive in 1375, but then, as the ODNB also says that Maud, Lady Burnell was the daughter of Earl Richard when she was certainly his sister (as proved by an entry on the Close Roll of 1283 regarding her marriage and a petition of her daughter Maud Haudlo in about 1330), it is hardly to be trusted on this point. Master John de Arundel in fact was dead by June 1331, when Pope John XXII provided other men, including Edward III's former tutor Richard de Bury, to his vacant benefices.  The confusion arises from Earl Richard's grandson and namesake Earl Richard of Arundel's will of 5 December 1375, which mentions "my dear uncle Sir John Arundell."  The identity of this John is uncertain, but it definitely wasn't the cleric John, who would have been an unlikely eighty-five years old in 1375. Given that no less a person than Pope John XXII informed numerous men that Master John was dead in June 1331, we may safely assume that he was dead in June 1331. The 'Sir John' of the 1375 will may have been an illegitimate son of Earl Richard, and perhaps born near the end of Richard's life in 1302, given that he was still alive in 1375.
Alice, Lady Segrave
Probably the second daughter of Earl Richard and Countess Alesia, and named in her father's inquisition post mortem as holding two parts of a messuage in Upton, Shropshire by his gift. Alice married Stephen, Lord Segrave, son of John, Lord Segrave (born 1256), whom Edward II appointed 'keeper of the land of Scotland', and Christiana de Plessetis. Stephen was probably born in 1285, as he was said to be forty at the time of his father's death in September 1325, and he and Alice had two sons: John, the elder and his father's heir, born in 1315, and Stephen.  Stephen the elder was an adherent of Earl Thomas of Lancaster in the first few years of Edward II's reign, but had switched sides to the king by the time of his campaign against the Contrariants in 1321/22, and in January 1321 was one of the men Edward sent to negotiate a new peace treaty with Robert Bruce. Stephen's brother-in-law Edmund, earl of Arundel granted manors in Derbyshire, Leicestershire and Warwickshire to Stephen's father John for him to regrant them to Alice and Stephen. 
Stephen Segrave had the misfortune to be constable of the Tower of London at the time that Roger Mortimer escaped in August 1323; he and "many others" at the Tower were said to have been "poisoned by artifice," i.e. sedated by Mortimer. Stephen was replaced as constable by Walter Stapeldon, bishop of Exeter, and although he was said to be "seriously ill" from the sedatives, Stephen and his father had to acknowledge a liability to pay Edward II 10,000 marks in exchange for a pardon, which came on 1 June 1324.  The two men died in 1325 in Gascony, where they were serving Edward II during the War of Saint-Sardos, John on 3 September and Stephen shortly before 12 December, leaving his ten-year-old son John as his heir. John the father sent a letter from Gascony to Hugh Despenser the Younger in early November 1324, which began "To the honourable and wise man and his very dear lord and cousin*, if it please him, his John, lord of Segrave, greetings, honours and as much very dear affection as he can give," a typically sycophantic way of addressing the powerful royal favourite to which even Despenser's social superiors the earls of Kent and Surrey were not immune. 
* As far as I can work out, Despenser and Segrave were third cousins or thereabouts; John's great-grandmother was Rohese Despenser.
In early March 1327, at the beginning of Edward III's reign, wardship of Alice and Stephen's son John was granted to Edward II's half-brother Thomas of Brotherton, earl of Norfolk, and sometime between then and 1336 Norfolk arranged John's marriage to his elder daughter, and ultimately his sole heir, Margaret. Marriage to a king's niece and granddaughter was an excellent match for John Segrave and considerably less brilliant for Margaret, but this is altogether typical of her father (as Brad Verity has pointed out in an article for Foundations, Thomas of Brotherton rarely acted in the best interests of himself and his family). John and Margaret had a son, John, who died young but who might otherwise have married the great heiress Blanche of Lancaster - they were betrothed by 4 May 1347, and isn't it fascinating to contemplate how different English history would be if Blanche had married John Segrave instead of John of Gaunt - and a daughter Elizabeth born in 1338, who married John, Lord Mowbray and had children. 
Alice, Lady Segrave, née de Arundel, was accused in 1334 of entering an enclosure in Sherwood Forest with her greyhounds and poaching deer  - like father, like daughter - and died on 7 February 1340 (the date was discovered by Douglas Richardson in the registers of Chaucombe Priory).
Margaret le Boteler (Botiller)
Supposedly the wife of William le Boteler or Botiller of Wem in Shropshire, but there is no contemporary evidence to prove that Earl Richard had a daughter named Margaret, only family pedigrees of later centuries (one of which calls her the daughter of 'Willm. Erle of Arundell') and William le Botiller's wife is not named as Margaret in any source I've seen. (I haven't seen any source which names his wife at all.) Assuming that the tradition of her parentage is correct, one might speculate that Margaret was the youngest of Earl Richard and Countess Alesia's children, as her (supposed) husband William le Boteler was born on 8 September 1298, and was succeeded by his son, another William, in late 1361. 
1) Thomas Wright, ed., The roll of arms, of the princes, barons, and knights who attended King Edward I to the siege of Caerlaverock, in 1300, pp. 21-22.
7) Cal Pat Rolls 1307-1313, p. 486; Cal Fine Rolls 1307-1319, p. 141; Cal Close Rolls 1307-1313, p. 469.
8) Cal Fine Rolls 1307-1319, p. 214.
9) Cal Pat Rolls 1324-1327, p. 192; Cal Fine Rolls 1319-1327, pp. 4, 101.
10) Cal Close Rolls 1307-1313, pp. 356, 347; Cal Close Rolls 1313-1318, p. 223; Cal Pat Rolls 1307-1313, p. 493; Cal Pat Rolls 1313-1317, pp. 95, 167, 521; Cal Fine Rolls 1307-1319, p. 219; Rotuli Parliamentorum, vol. 1, p. 340; Calendar of Inquisitions Miscellaneous 1308-1348, p. 55.
11) Calendar of Papal Letters 1305-1341, p. 8.
12) Papal Letters 1305-1341, pp. 201, 294, 310; Cal Inq Misc 1308-1348, pp. 333-334; Calendar of Chancery Warrants 1244-1326, pp. 320, 560; Cal Pat Rolls 1307-1313, p. 278.
13) Papal Letters 1305-1341, pp. 327-328.
14) Testamenta Vetusta, vol. 1, p. 94.
15) C. Moor, Knights of Edward I, vol. 4, pp. 236-239; Berkeley Castle Muniments D/5/1/15.
16) Cal Pat Rolls 1317-1321, pp. 554, 567; BCM D/5.
17) Cal Fine Rolls 1319-1327, pp. 196, 232; Cal Pat Rolls 1321-1324, p. 425; Cal Close Rolls 1323-1327, pp. 13-14, 189.
18) Cal Fine Rolls 1319-1327, pp. 362, 371; Pierre Chaplais, ed., The War of Saint-Sardos (1323-1325): Gascon Correspondence and Diplomatic Documents, p. 88.
19) Cal Pat Rolls 1327-1330, p. 23; Berkeley Castle Muniments D/5/101/8: "John de Segrave and Henry earl of Lancaster. Fri. after the Invention of Holy Cross, 21 Edw. III. Whereas John's son John and Henry's daughter Blanche have been espoused, John has entered into a bond of £5,000 a year to Henry."
20) Peter Coss, The Lady in Medieval England 1000-1500, p. 67.
21) Cal Fine Rolls 1356-1368, pp. 201, 209.