Edward II and Queen Isabella's elder daughter was born at Woodstock near Oxford on 18 June 1318, having been conceived the previous autumn when Edward and Isabella were together at York, and named after her paternal grandmother Eleanor of Castile. Edward had been on pilgrimage in Canterbury, but managed to arrive at Woodstock on the day of his daughter's birth, and paid 500 marks to "the Lady Isabella, queen of England, of the king’s gift, for the feast of her purification after the birth of the Lady Alienora her daughter."  Notice that Eleanor was called 'Lady', not 'Princess'.
Shortly after her birth, little Eleanor of Woodstock went to live at Wallingford Castle with her elder brothers Edward of Windsor (five years seven months her senior) and John of Eltham (one year ten months her senior), under the care of a nurse named Joan du Bois. John and Eleanor remained "in the company" of their brother Edward of Windsor, "at his expenses."  On 31 October 1318, Edward granted the castle and honour of High Peak in Derbyshire, the manors of Macclesfield and Overton in Cheshire, the manors of 'Rosfeyr, Dolpenmayn and Pennaghan' in Wales, and others to "John his son and Eleanor, sister of the said John...to hold for their sustenance at the king's will."  On 1 June 1320, Edward granted High Peak to Queen Isabella, "to hold in aid of the expenses of John, the king’s son, and Eleanor his sister, the king’s daughter," which may suggest that the household of the younger royal children was attached to the queen's.  This 1320 grant of High Peak to Isabella is the sole evidence that her younger children were living with her in the autumn of 1324, when Edward established separate households for them and thus - oh, the cruelty!!! - 'removed' Isabella's children from her. As though a medieval queen or noblewoman was expected to raise her own children anyway. Edward II was the legal guardian of his children, not Isabella, and harsh though it may seem from a modern perspective, medieval royal and noble women had few if any rights over their children. Some writers, in their rush to present Isabella as a victim, conveniently ignore the essential differences between medieval and modern motherhood.
Edward and Isabella's second daughter Joan was born at the Tower of London on 5 July 1321, when Edward was thirty-seven and Isabella twenty-five or twenty-six, and named after her maternal grandmother Joan (Jeanne) of Navarre. A man named Robert de Staunton was granted a respite of £80 on a debt of £180 he owed the Exchequer for the simple expedient of travelling a couple of miles across London to inform Edward II.  Edward arrived at the Tower three days later, and stayed there with his wife and baby daughter for the next six days. The Tower was in a somewhat dilapidated state, and rain came in on Isabella's bed when she was in labour. A furious Edward dismissed the constable of the Tower, John Cromwell, from his post.
Joan of the Tower had a nurse named Matilda Pyrie or Perie, formerly the nurse of her brother John of Eltham, and presumably lived in the same household as her elder siblings, or some of them.  Presumably, again, Edward visited his children occasionally, and sent them gifts, and presumably yet again, they visited court sometimes too, but I haven't been able to find any details. The lives of medieval children are really obscure, even the king's children. It's almost impossible to find any personal details about Edward's daughters.
In September 1324, Edward II established separate households for his three younger children, and Eleanor (de Clare) Despenser became the guardian of John of Eltham, aged eight. Eleanor was Edward's niece and thus John's first cousin, and as the eldest granddaughter of Edward I was an entirely appropriate person to take responsibility for the king of England's son. Ralph de Monthermer and Isabel Hastings became the guardians of Eleanor of Woodstock and Joan of the Tower, now six and three, who lived with the couple at Marlborough.  Ralph was Edward's former brother-in-law, having married Edward's sister Joan of Acre in early 1297, which means that Edward had known Ralph, who joined the king's family circle when Edward was only twelve, for nearly thirty years. Ralph's wife Isabel Hastings was the sister of Edward's favourite Hugh Despenser, which might have been a factor in Edward's decision, but evidently she was a trustworthy, maternal type: when Edward's niece Elizabeth (de Clare) de Burgh attended his funeral in December 1327, she left her two young daughters in Isabel's care, despite her hatred of Isabel's late brother.  After Ralph's death in early 1325, Isabel remained in charge of the royal sisters' household. 
In January 1325, Edward II turned his attention to the important question of his daughters' marriages, and opened negotiations with Castile for Eleanor of Woodstock to marry Alfonso XI.  Alfonso was born on 13 August 1311, seven years Eleanor's senior, and succeeded his father Fernando IV on 7 September 1312, at less than a year old. At the same time, Edward arranged the future marriage of his eldest son and heir Edward of Windsor to Alfonso XI's sister Leonor, "to make a treaty of friendship with the said king and his guardians and the rest of the magnates of Spain [i.e. Castile] and other realms, commonalties and universities."
Alfonso - or rather his advisors, given that he was only thirteen - declared that he "desires that his royal house shall be joined to the king's by a treaty of love by way of relationship."  Edward II, carried away with enthusiasm for his first cousin twice removed (Alfonso was the great-great-grandson of Edward's grandfather Fernando III), responded "The king rejoices greatly that providence has illuminated abundantly the boldness of Alfonsus's youth by gifts of virtues and natural and gracious good things, as widely diffused fame has made known and is as now spread to the ends of the world."  (Bear in mind that this renowned paragon of virtue was a thirteen-year-old boy.)
A few weeks later, Edward wrote to his cousin the lady of Biscay about the marriages, including the great quote I've already cited here a while back about his "rejoicing at the clinging together of such progeny sprung from his and her common stock, whilst they applaud each other with mutual honours and cherish each other with mutual counsel and aid." Edward also wrote to another cousin, don Juan, that "The king has received his letters with joy...[Juan] not only shows himself ready and prepared for the king's [Edward's] will and pleasure, but also asserts that nothing more pleasing or desirable could be offered to him than to perfect and execute those things that are to the king's advantage and honour, according to the king's desire."  On another occasion, he wrote to another of his Castilian cousins named Juan, declaring that he "recognised the abundance of Sir John's grace" and thanking him for his promise to raise 1000 knights and 10,000 footmen and squires to aid Edward in his war against France. 
At the same time, Edward went ahead with plans to marry Joan of the Tower to the grandson of the reigning king of Aragon, Jaime II, and sent envoys to discuss the "espousals...of the king's daughter Joan with the first-born of Alfonso the eldest son of James king of Aragon, and the future heir of Aragon."  The said grandson was born in September 1319, so was less than two years older than Joan, and succeeded his father as King Pedro IV of Aragon in 1336. Pedro lived until 1387 and is known as El del Punyalet, 'he of the little dagger'. He was also king of Sardinia, Corsica and Valencia and count of Barcelona, and, many years later, duke of Athens. Pedro and Joan were third cousins, both great-great-grandchildren of King Jaime I of Aragon, via Queen Isabella (and also third cousins once removed via Edward II).
"And because it was said that James is old and decrepit and it is not certain that he is not dead" - in fact, Jaime lived until November 1327 - Edward instructed his proctors to treat with Alfonso, Jaime's eldest son and Alfonso IV of Aragon from 1327 to 1336. No doubt Edward was pleased at the thought of an Aragonese marriage for his younger daughter, but, apart from his statement that "the king is eager that a confederation or alliance of love shall be made in some suitable way between himself and James," there's absolutely none of the 'rejoicing' and enthusiasm in the letters between himself and Castile.  Given that Edward II was half-Castilian himself, this is hardly suprising. Of course the Spanish alliances were political first and foremost - England and France were at war over Gascony in 1324/25, and both Aragon and Castile would be useful allies. But the tone of Edward II's long, well-informed and highly enthusiastic letters to Castile strongly suggest that he was genuinely delighted, on a personal level, at the thought of two of his children marrying into Castile.
Because of Edward's deposition less than two years later, none of these Spanish alliances came to pass. Alfonso XI of Castile married Maria of Portugal, had three or four children, and died of plague in 1350. Pedro IV of Aragon married four times: Marie of Navarre (granddaughter of Queen Isabella's brother Louis X), Leonor of Portugal (sister of Maria who married Alfonso XI), Eleanor of Sicily and Sibila of Fortià. His two successors, Juan I and Martí I, were the sons of his third wife Eleanor.
Eleanor of Woodstock made a not terribly brilliant marriage to Reynald II, count and later duke of Gelderland, in May 1332, the month before her fourteenth birthday, had two sons, and died aged thirty-seven in 1355. Joan of the Tower married Robert Bruce's son the future David II of Scotland in 1329, as part of her mother and Mortimer's detested peace treaty with Bruce. She died childless in 1362. Neither woman's marriage could be said to be particularly successful, and it's interesting to speculate what might have happened if the planned Spanish marriages had gone ahead instead.
1: Thomas Stapleton, ‘A Brief Summary of the Wardrobe Accounts of the tenth, eleventh, and fourteenth years of King Edward the Second’, Archaeologia, 26 (1836), p. 337.
2: Calendar of Fine Rolls 1307-1319, p. 389 and CFR 1319-1327, p. 6, that John and Eleanor lived with Edward; Calendar of Patent Rolls 1327-1330, p. 163, for Joan du Bois and Matilda Perie.
3: CPR 1317-1321, pp. 222-223.
4: CPR 1317-1321, p. 453.
5: CPR 1321-1324, p. 23.
6: CPR 1324-1327, p. 88.
7: Frances A. Underhill, For Her Good Estate: The Life of Elizabeth de Burgh (1999), pp. 40-41.
8: CPR 1324-1327, pp. 157, 243.
9: Calendar of Close Rolls 1323-1327, pp. 344, 350-351; CPR 1324-1327, pp. 103-4; The National Archives C 47/27/13/15 and C 47/27/13/16.
10: CCR 1323-1327, p. 344.
12: CCR 1323-1327, p. 350.
13: CCR 1323-1327, p. 344.
14: CPR 1324-1327, pp. 103-104.
15: CCR 1323-1327, p. 359.