Married first, 9 Sept 1359 Elizabeth Bohun daughter of William Bohun, 1st Earl of Northampton  of the March 1336/7 creation
Married second, 15 Aug 1390 Philippa Mortimer, daughter of 3rd Earl of March by Philippa, only daughter of Lionel Duke of Clarence (2nd son of Edward III), and widow of 5th Lord (Baron) Hastings. He was attainted, his titles and lands being forfeited, and beheaded 21 Sep 1397 for his opposition to Richard II, having had no issue by her [Philippa].
At coronation of Richard II, in 1377, FitzAlan carried the crown. 
1377: Admiral of West and South.
1378: attacked Harfleur at Whitsun 1378, but forced to return to his ships by the defenders. Later, he and John of Gaunt attempted to seize Saint-Malo but were unsuccessful.
closely aligned with Thomas, Duke of Gloucester -- uncle of King Richard II. Thomas opposed Richard II's desire for peace with France in the Hundred Years War and a power struggle ensued with Gloucester.
1386: Richard II named him Admiral of England, as well as being made a Knight of the Garter.
Aug 1386: King dismissed Gloucester and FitzAlan from Council
late 1386: Gloucester forced Richard II to name him and Richard FitzAlan to Richard's Council -- a Regency Council for Richard II -- but Richard limited duration of Council powers to one year.
Mar 1387: As Admiral of England, he defeated a Franco-Spanish-Flemish fleet off Margate, along with Thomas de Mowbray, Earl of Nottingham.
King summoned Gloucester and FitzAlan to meeting, but instead of coming, they raised troops and defeated the new Council at Radcot Bridge, taking the favorites prisoner. The Merciless Parliament the next year condemned the favorites. FitzAlan was one of the Lords Appellant who accused and condemned Richard II's favorites. He made himself particularly odious to Richard by refusing, along with Gloucester to spare the life of Sir Simon Burley who had been condemned by the Merciless Parliament, even though the queen, Anne of Bohemia went down on her knees before them to beg for mercy.
1394: antagonized King by arriving late for queen's funeral ... Richard, in a rage snatched a wand and struck him in the face and drew blood. Shortly after, Richard feigned reconciliation.
1388: named Governor of Brest
1389: Peace with France, but FitzAlan followed Gloucester and stated he would not agree.
↑ On 12 July 1397 he was arrested for his opposition to Richard II, as well as plotting with Gloucester to imprison the king. He stood trial at Westminster and was attainted. He was beheaded on 21 September 1397 and was buried in the church of the Augustin Friars, Bread Street, London.
Tradition holds that his final words were said to the executioner, "Torment me not long, strike off my head in one blow". In October of 1400, the attainder was reversed, and Richard's son Thomas succeeded to his father's estates and honors.
↑Royal Ancestry: A Study in Colonial and Medieval Families, vol II, page 611
↑ replaced them with his favourites - including Archbishop of York, Alexander Neville, Duke of Ireland Robert de Vere, Michael de la Pole the Earl of Suffolk, Sir Robert Tresilian who was the Chief Justice, and the former Mayor of London Nicholas Brembre.
Royal Ancestry by Douglas Richardson Vol. IV page 188
It may be possible to confirm family relationships with Richard by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
The Magna Carta project follows EuroAristo naming guidelines... "de Arundel" was more place than surname for him. And from Richardson's Magna Carta Ancestry, Vol III, p 336 "...by Eleanor, daughter of Richard Fitz Alan (or de Arundel), Knt., 8th Earl of Arundel."