Thomas of Brotherton was born on 1 June 1300 as the eldest of the three children of King Edward I, then aged almost sixty-one (born 17 June 1239), and his second queen Marguerite of France, daughter of Philip III and younger half-sister of Philip IV. Thomas, who was sixteen years younger than his half-brother Edward II, was followed by a brother Edmund of Woodstock, later earl of Kent (5 August 1301 - 19 March 1330) and a short-lived sister Eleanor (May 1306 - October/November 1311), who was born when their father Edward I was almost sixty-seven. By way of comparison, Edward I's eldest great-grandchild Hugh, Lord Despenser (d. 1349), son of Eleanor de Clare and Hugh Despenser the Younger, was born in 1308 or 1309: only two or three years between a child and a great-grandchild. Thomas of Brotherton was seven when his father died on 7 July 1307, and was heir to the English throne from that day until the birth of his nephew, Edward II and Isabella of France's son the future Edward III, on 13 November 1312. Perhaps by way of consolation, Edward II created his twelve-year-old half-brother earl of Norfolk a month later.  Thomas was an executor of his mother Queen Marguerite's will after her death on 14 February 1318, and was knighted by Edward II in Newcastle on 15 July 1319. 
Twenty-year-old Thomas was still unmarried on 16 August 1320, when he went to Langley in Hertfordshire to meet the king - recently returned from a trip to France to pay homage to his brother-in-law/Thomas's first cousin Philip V for his French lands - and discuss or ask advice about his marriage. Edward II told Thomas to come back to him again sometime later at Clarendon and wrote about it to their kinsman Aymer de Valence, earl of Pembroke, who would join him at Clarendon, "because in this matter...we do not wish to hear or do anything without your counsel" (pur ce qe en cele chose...nous ne voloms ouir ne rien faire saunz vostre conseil, my translation).  King Jaime II of Aragon had proposed his daughter Maria (born 1299), widow of Pedro of Castile, as Thomas's bride, but in August 1321 reported to Edward that Maria had decided to take the veil and that he did not think he would be able to change her mind.  (Pedro of Castile was the son of Sancho IV and younger brother of Fernando IV and thus Edward II's first cousin once removed via Edward's mother Eleanor of Castile, and was killed at the battle of Vega de Grenada in June 1319. And it's interesting to see that Maria of Aragon went her own way here, chose her own fate and decided she didn't want to remarry, and that her father didn't force her to obey his will even when it meant allying with a powerful country.) At the same time, Edward II and Jaime II were involved in negotiations for Edward's son Edward of Windsor, the future Edward III, to marry Violante (born 1310), another of Jaime's daughters, though ultimately nothing came of it; both marriages were proposed by Pierre Galicien, Edward II's treasurer of the Agenais in Gascony, and Vidal Villanova, a councillor of Jaime II.  Thomas of Brotherton must have been aware of these negotiations for his marriage in Aragon, as he was with Edward at Gloucester on 28 March 1321 when the king sent his envoy to Spain to continue them. 
At some point after the negotiations with Aragon, Thomas married Alice Hailes, daughter of Roger Hailes, coroner of Norfolk. It was an extraordinary marriage for a man who was, as I said above, son and brother of kings of England and nephew of a king of France, and whose marriage to the king of Aragon's daughter had been proposed and discussed. Thomas turned twenty-one and thus came of age on 1 June 1321, and perhaps married Alice Hailes shortly after learning that Maria of Aragon was not available that August. As to why a king's son would want to marry a woman of obscure family, with no lands, wealth or powerful connections, I cannot imagine. Presumably it must have been a love, or lust, match, but in that case - sorry for being crude - Thomas could merely have taken Alice as his mistress rather than his wife. However romantic a king's son marrying a woman of his choice so much farther down the social scale might seem to us, to Thomas's contemporaries it must have seemed entirely unaccountable, and deeply foolish.
Thomas of Brotherton and Alice Hailes had three children. Their only son was Edward, who married Beatrice, one of the youngest of the eight daughters of Roger Mortimer, earl of March, and Joan Geneville, in 1329. Edward can't have been more than five or six at the time, Beatrice presumably some years older (Roger's imprisonment at the Tower of London in February 1322 and his escape to the Continent in August 1323 necessarily ended his marital relations with Joan, and their twelve children must have been born before his imprisonment). Edward of Norfolk sadly died as a child in 1334, or perhaps even 1332 or 1333; the date, as with so much else in Thomas of Brotherton's life, is not recorded, but Edward's young widow Beatrice Mortimer had married her second husband Thomas Braose by 2 December 1334.  There were also two daughters of Thomas and Alice Hailes' marriage: Alice, the younger, and Margaret. Alice married Sir Edward Montacute (died 1361), youngest son of Edward II's friend Sir William Montacute (died 1319); Edward's elder brother William (died 1344) was earl of Salisbury, and another brother, Simon, was bishop of Worcester and Ely. Edward Montacute must have been close to twenty years older than Alice, given that his elder brothers Earl William and Bishop Simon were born in 1301 and 1303/04 respectively, and Alice was born in or after 1323 (I don't know, and I don't know if anyone knows, if she was older or younger than her brother Edward). Alice had in fact been betrothed to the earl of Salisbury's son John, but when he died suddenly, his uncle Edward Montacute was substituted and married her instead. This was to prove tragic for poor Alice: in the early 1350s her husband beat her so badly she died of her injuries, and, although Alice was the first cousin of Edward III, Montacute suffered no penalty whatsoever for this vile act. Alice had several children, who died quite young.
The date of birth of Margaret of Norfolk (also known as Margaret Marshal and Margaret of Brotherton), Thomas of Brotherton and Alice Hailes' eldest child, is almost invariably given as c. 1320, but given what I wrote above about the negotiations with Aragon for her father's marriage in 1320/21, that's too early. A date of birth of 1322 for Margaret would seem about right, probably the year after her parents' marriage. It can't be pushed back later than 1323 or 1324 as her own first child was born in 1338. Margaret, niece of Edward II, first cousin of Edward III, married John, Lord Segrave (born 1315), whose father Stephen (died 1325) had been Constable of the Tower of London in August 1323 when Roger Mortimer escaped. Thomas of Brotherton was granted the wardship and marriage of the twelve-year-old John Segrave on 3 March 1327, early in the regency of Mortimer and Isabella, and, so the entry on the Patent Roll states, "for service to queen Isabella."  It was logical, therefore, for Thomas to arrange his daughter's marriage to his ward. The Segraves held reasonably extensive lands but were hardly among the first rank of the nobility, and arranging his daughter's marriage to John seems therefore not to have been a great decision on Thomas of Brotherton's part, which isn't surprising when we look at his life and career and choices in general. John Segrave died in April 1353, and shortly before 30 May 1354 Margaret married secondly a man far more to her liking and by her own choice, without her cousin Edward III's permission: Walter, Lord Manny or Mauny, a Hainaulter who probably came to England in 1328 with Queen Philippa (of Hainault).
When Thomas of Brotherton, earl of Norfolk, died on 4 August 1338, his elder daughter Margaret, then aged perhaps sixteen, succeeded as countess of Norfolk in her own right, and also as hereditary Lord or Earl Marshal of England. With the exception of her four greats granddaughter and heiress Anne Mowbray, who died as a child in 1481, Margaret is the only woman in English history to have held this office. Richard II, great-grandson of Margaret's uncle Edward II, created her duchess of Norfolk in her own right on 29 September 1397, the first English woman in history to be a duchess in her own right. (The first English duchess in history was Isabella Beaumont, wife of Henry of Grosmont, made duke of Lancaster in 1351.) Duchess Margaret died on 24 March 1399, when she must have been in her late seventies, the last surviving of Edward I's grandchildren; her cousin Margaret de Bohun, countess of Devon, who lived till December 1391, was the second longest survivor.
Two of Margaret's six or seven children, both daughters, lived long enough to marry and have children, although Margaret outlived both of them. One was Anne Manny, born on 24 July 1355, who married John Hastings, earl of Pembroke (born 1347) - grandson of Roger Mortimer and Joan Geneville via their daughter Agnes, and widower of Edward III's daughter Margaret (died 1361) - with whom she had one child, also John Hastings, earl of Pembroke, born in 1372 and killed jousting in 1389. Although this John was only seventeen when he died, he had been married twice: to the much older Elizabeth of Lancaster, daughter of John of Gaunt and granddaughter of Henry of Grosmont, which marriage was annulled; and secondly to Philippa Mortimer, great-granddaughter of Edward III. John died childless, and that was the end of the Norfolk-Manny-Hastings line. It was also the end of the genealogical line of one of my favourite women of the fourteenth century, Juliana Leyburne, who was the paternal grandmother of John Hastings, earl of Pembroke born in 1347.
Margaret of Norfolk's other surviving daughter was her eldest child Elizabeth Segrave, born on 25 October 1338 when Margaret was probably fifteen or sixteen. Elizabeth married John, Lord Mowbray, born on 25 June 1340, one of the many grandchildren of Edward II's first cousin Henry of Lancaster. John Mowbray died in his late twenties on crusade near Constantinople, leaving his and Elizabeth's elder son John who died as a teenager, a younger son Thomas born in 1366, and four daughters, one of whom was abbess of Barking. Thomas Mowbray, heir to the Mowbrays, the Segraves and the earldom/dukedom of Norfolk, was made earl of Nottingham by Richard II in 1386 but perpetually banished from England by him in 1398 following a quarrel with the future Henry IV, and died in Venice the following year. He had become duke of Norfolk in the meantime on the death of his elderly grandmother Margaret of Norfolk on 24 March 1399. Thomas married Elizabeth, daughter of the earl of Arundel executed by Richard II in 1397, and his descendants were dukes of Norfolk in the fifteenth century, as Margaret of Norfolk's heirs. Thomas Mowbray's son and heir John, duke of Norfolk (1392-1432) married in 1412 a woman, Katherine Neville (born c. 1400), who lived long enough to attend her nephew Richard III's coronation in 1483. It's rather astonishing to me that a man born in Edward III's reign had a daughter-in-law who lived into Richard III's reign.
1) Calendar of Charter Rolls 1300-1326, p. 205.
2) Oxford Dictionary of National Biography.
3) J.R.S. Phillips,Aymer de Valence, earl of Pembroke 1307-1324: Baronial Politics in the Reign of Edward II (1972), pp. 190-191, citing The National Archives SC 1/49/49.
4) Pierre Chaplais, English Medieval Diplomatic Practice (1982), part 1, vol. 1, pp. 63-66.
6) Alison Marshall, 'Thomas of Brotherton, Earl of Norfolk and Marshal of England: A Study in Early Fourteenth-Century Aristocracy', PhD dissertation, Univ. of Bristol, 2006, p. 78.
7) Calendar of Patent Rolls 1334-1338, p. 62; Brad Verity, 'Love Matches and Contracted Misery: Thomas of Brotherton and his Daughters (Part 1), in Foundations, the Journal of the Foundation for Medieval Genealogy (2006), 2 (2), pp. 91-110 (p. 105).
8) Patent Rolls 1327-1330, p. 23.