Joan Gaveston's maternal grandparents were Edward I's second daughter Joan of Acre (1272-1307) and Gilbert 'the Red' de Clare, earl of Gloucester (1243-1295); her paternal grandparents were Sir Arnaud de Gabaston, baron of Béarn (d. 1302) and Claramonde de Marsan (d. 1287), daughter of Arnaud-Guilhem de Marsan, baron of Gascony. She was presumably named after her grandmother Joan of Acre, and as well as being his beloved Piers' daughter and heir, was also Edward II's great-niece. He had become a great-uncle at the ridiculously young age of twenty-four or twenty-five, at the birth of Eleanor de Clare and Hugh Despenser the Younger's first child Hugh in 1308 or 1309 (Edward I's eldest great-grandchild). In York on 20 February 1312, after Margaret's churching – the purification ceremony forty days after childbirth – Edward and the proud parents celebrated the birth of Piers' first legitimate child (as far as anyone knew then, he was likely to have more). Edward paid out the huge sum of forty marks to celebrate Margaret's purification, and the guests were entertained by his minstrel 'King Robert'.  He and Isabella conceived Edward III (born 13 November 1312) around this time.
Margaret de Clare was probably seventeen when she gave birth to Joan. The fact that she and Piers only had one child, born over four years after their wedding, has been used by some commentators as evidence that they rarely slept together or had an unhappy marriage (Natalie Fryde calls Margaret "tragic," for example). I don't agree. Margaret's date of birth is not known, but her elder siblings Gilbert and Eleanor were born in May 1291 and October/November 1292, and her younger sister Elizabeth was born in September 1295. The likeliest date of Margaret's birth is the spring or summer of 1294, and therefore she was thirteen when she married Piers on 1 November 1307 - young enough so that she most likely hadn't yet become fertile. Her sisters Eleanor and Elizabeth were also both thirteen when they married Hugh Despenser the Younger on 26 May 1306 and John de Burgh on 30 September 1308 respectively. Eleanor's first child Hugh was born two or three years after her wedding sometime in 1308 or 1309, and Elizabeth's first child William was born four years after her wedding in September 1312, the day after her seventeenth birthday. Isabella of France was twelve when she married Edward II on 25 January 1308 and conceived their first child just over four years later. Joan Gaveston must have been conceived in about April 1311, which may have been around the time of Margaret de Clare's seventeenth birthday. Margaret's aunt by marriage Queen Isabella and her sisters Eleanor and Elizabeth married at twelve or thirteen and first became pregnant at sixteen (perhaps fifteen in Eleanor's case, as her son Hugh's date of birth cannot be narrowed down to a month), so Margaret was hardly far behind the norm in her family. In any case, we don't know for certain that Joan was her first pregnancy, only that she was her first surviving child, and previous miscarriages can't be ruled out. She had only one child, Margaret Stafford née Audley, by her second husband Hugh Audley as well. Margaret the daughter's date of birth is not known, but must have been sometime between early 1318 (nine months after Hugh and Margaret's wedding on 28 April 1317) and late 1322 (nine months after Edward II imprisoned Hugh as a Contrariant). As Margaret the daughter was abducted and forcibly married by Ralph Stafford in January or February 1336, I tend to assume that she was born in 1320 or later rather than 1318, as it would be odd if such a great heiress had reached the age of seventeen or eighteen and was not yet married. This would mean that Margaret de Clare also took several years to become pregnant or to bear a living child in her second marriage, and that therefore, the supposed 'delay' in becoming pregnant by Piers doesn't say anything negative about her relationship with him.
Joan Gaveston was only five months old when her father was killed at Blacklow Hill on 19 June 1312. As Piers had been a tenant-in-chief - i.e. he held land directly of the king - Edward II as the king became her legal guardian, as per the rules of the time. Edward sent her to live at Amesbury Priory in Wiltshire with her cousin Eleanor de Bohun, future countess of Ormond, daughter of Edward's sister Elizabeth and the earl of Hereford (one of the men present at Piers Gaveston's execution, in fact). The king provided generously for the girls' upkeep. They had relatives at the priory, which had become fashionable among royal ladies since the dowager queen Eleanor of Provence retired there in the 1280s: Edward II's sister Mary was a nun there, as were Joan Gaveston's aunt Joan de Monthermer (her mother's half-sister, one of Joan of Acre's five daughters) and Henry of Lancaster's daughter Isabella. Other royal and noble ladies appear to have lived at Amesbury temporarily on occasion: Joan Gaveston's aunt Elizabeth de Clare stayed there for a year or so after her marriage before she went to Ireland to join her husband, and again when she was pregnant with her second child Isabella de Verdon. So Joan likely had plenty of her relatives about and didn't lack for company.
Joan was two years old when her uncle Gilbert de Clare, earl of Gloucester was killed at the battle of Bannockburn in June 1314. As the only child of one of Gilbert's three sisters and co-heirs, she became an enticing marriage prospect. In 1316, Edward offered her to his ward Thomas, future Lord Wake of Liddell, who was then eighteen or nineteen (and the brother of the future countess of Kent). However, Edward discovered that Wake had married Henry of Lancaster's eldest daughter Blanche without his permission, and fined him a large sum, probably £1000, which he granted to "our very dear relative," Joan.  In November 1317, Wake paid 1000 marks (£666) in "part satisfaction" of the fine. As he had no means of raising such a large sum – he was still under twenty-one and hadn't yet come into his lands – he probably had to borrow the money from his father-in-law Henry, the earl of Lancaster's brother, or Lancaster himself; a nice way for Edward to get money out of his enemy and give it to Piers Gaveston's daughter. It is somewhat odd that Wake chose Blanche of Lancaster in preference to Joan, as Blanche had a brother and thus would not inherit anything from her father or uncle, while Joan was then sole heir to a third of the vast de Clare inheritance. Perhaps Wake gambled that Margaret de Clare would marry again and have a son and that Joan Gaveston ultimately wouldn't inherit anything, and that it was more advantageous in the political climate of 1316 to be allied to the earl of Lancaster than to Edward II. Margaret in fact had another daughter, but no son, which would have meant that the two half-sisters Joan Gaveston and Margaret Audley shared the inheritance equally as her joint heirs (primogeniture not applying to women).
On 25 May 1317, Edward II arranged Joan Gaveston's future marriage to John, son and heir of Thomas Multon, lord of Egremont in Cumberland. John, born in 1308, was the eldest grandson of Richard de Burgh, earl of Ulster (d. 1326) via his mother, and nephew of Elizabeth de Burgh, queen of Scotland and Gilbert de Clare's widow Maud, dowager countess of Gloucester (the lady who pretended to be pregnant by Gilbert for years after Bannockburn). John's other aunts included the countesses of Louth, Desmond and Kildare. In the agreement between the king and Thomas Multon, Joan is called "daughter of Sir Piers Gaveston, formerly earl of Cornwall" (Johane la feile monsieur Piers de Gavaston, jadys counte de Cornewayll). The marriage of John and Joan would take place "as soon as the said children shall be of reasonable age" (si tost come les ditz enfauntz serront venuz a age covenable, qils peussent estre marietz). Thomas Multon agreed to grant Joan 400 marks' worth of land yearly, and promised the king that "he will not eloign from himself any lands that he now holds or that he shall inherit by reversion or otherwise, to the damage or disinheritance of his son," though presumably it wasn't John Multon's disinheritance that Edward cared about, but Joan Gaveston's. He intended for Joan to go and live with the Multons – though apparently she didn't – and ordered Thomas Multon to maintain her honourably, "as it shall please our lord the king or other friends of the said Joan." Edward agreed to give Multon £1000 for Joan's dowry, in three instalments of 500 marks, the first payable immediately, the second on 24 June (Nativity of St John the Baptist) and the third on29 September (Michaelmas). Edward did not in fact pay this money to Multon; Thomas Wake did so on his behalf, "for refusing a suitable marriage, which the king offered to him, and marrying elsewhere without licence." Multon had to promise to pay the king the staggeringly large sum of £10,000 if he defaulted on his son's marriage – proof of Edward's determination that this match he had arranged for Piers Gaveston's daughter should succeed where the first hadn't. 
After this, Joan Gaveston remains obscure until she died suddenly at Amesbury Priory on 13 January 1325, of an unknown illness. This may have been the day after her thirteenth birthday. I very much doubt that Edward II would have let the death of Piers Gaveston's child and his own great-niece pass without making expensive and elaborate funerary arrangements for her, though sadly no record of such is still extant. Edward spent, for example, considerable amounts of money on the funeral of his friend William Montacute's teenaged son John in 1317, and seems to have been particularly affected by John's death. It's hard to imagine that he felt less sorrowful at the death of Piers' thirteen-year-old daughter.
Joan's marriage to John Multon, who was sixteen or seventeen when she died, had not yet taken place. (John was destined to die childless in 1334, leaving his three sisters as his co-heirs.) An inquisition taken in January 1332 - which was probably commissioned in order to ascertain whether John Multon owed any of the £10,000 penalty agreed by his father and Edward II to Edward III, which he didn't as he hadn't defaulted on the marriage - states vaguely that Joan "died of illness" and also, wrongly, that she was fifteen at the time of her death.  This discrepancy of two years, easily explicable by the fact that the two men sitting on the inquisition seven years after Joan's death had almost certainly never met her and were going on hearsay of how old some people thought she might have been, in a world where birth certificates and parish records of births did not yet exist, was used by some commentators on soc.genealogy.medieval a few years ago to create endless confusion with Joan's half-sister Amie, Piers' other daughter, who was certainly not Margaret de Clare's daughter and thus must have been illegitimate. Amie Gaveston was a damsel of Queen Philippa's chamber, granted lands by the queen in 1332 (the entries relating to this are on the Patent Roll), and in 1334 called "Amie, daughter of Piers Gaveston", Amie filie Petri de Gauaston. The endless and for the most part astonishingly pointless debate about Amie - if you go to Google groups and search for 'Amie/Amy Gaveston' you'll find it - resulted in such craptacular statements as "just because she [Amie] was called the daughter of Petrus de Gaveston did not make her his blood relation." Yeah, happens all the time, doesn't it, that someone named in an official document as the child of someone else wasn't actually a blood relative of that person. Seems that some people have trouble imagining that Piers, the beloved of Edward II, might have fathered an illegitimate child, but given that Edward II himself certainly did, it's hardly to be wondered at that Piers did too. Another classic ('classic' here meaning 'totally bonkers') argument from a few years back was that 'Amie, daughter of Piers Gaveston' was in fact the illegitimate daughter of Margaret de Clare. Ho ho ho, I'm still laughing at that one. From some extremely knowledgeable comments left on my blog recently by a lovely anonymous commenter (thank you!), I now know that Piers Gaveston had a sister named Amie or Amye, born in 1285 - I'd thought before that she was in fact called Amie, but had no evidence. This makes it pretty well certain that the Amie Gaveston found on record in the 1330s said to be Piers' daughter was indeed his daughter (what a surprise!), whom he named in honour of his younger sister. (Who, according to the Vita Edwardi Secundi, naming her only as 'his sister', was with him during the siege of Scarborough in May 1312.) Both Edward II and Piers Gaveston fathered children by two women each that we know of, as well as carrying on their own intense relationship. The mothers of their illegitimate children are unknown.
RIP, Joan Gaveston. I wish you'd lived longer. I wish your father had lived longer.
1) Gesta Edwardi de Carnarvon Auctore Canonico Bridlingtoniensi, in W. Stubbs, ed., Chronicles of the Reigns of Edward I and Edward II, volume 2 (1883), p. 42; Pierre Chaplais, Piers Gaveston: Edward II’s Adoptive Brother, pp. 78-79; J.S. Hamilton, Piers Gaveston, Earl of Cornwall 1307-1312: Politics and Patronage in the Reign of Edward II, pp. 93-94.
2) F. D. Blackley and G. Hermansen, eds., The Household Book of Queen Isabella of England, p. 139.
3) Elizabeth Hallam, The Itinerary of Edward II and His Household, 1307-1328, p. 81; Calendar of Chancery Warrants 1244-1326, p. 382; Chaplais, Gaveston, pp. 77-78.
4) Constance Bullock-Davies, A Register of Royal and Baronial Domestic Minstrels 1272-1327, p. 143.
5) Calendar of Patent Rolls 1313-1317, p. 553; Cal Pat Rolls 1317-1321, p. 43; Calendar of Close Rolls 1313-1318, p. 468; Foedera 1307-1327, pp. 299, 331.
6) Cal Pat Rolls 1317-1321, p. 43; Foedera, p. 331.
7) Calendar of Inquisitions Miscellaneous 1308-1348, pp. 325-326.