From Wikipedia: William d’Aubigny, 2nd Earl of Arundel

William d'Aubigny, 2nd Earl of Arundel (b. [1138-1150], d. 24 December 1193), also called William de Albini III,[1] was the son of William d'Aubigny, 1st Earl of Arundel and Adeliza of Louvain, widow of Henry I of England.[2]
He married Matilda St Hilary de Harcouët and among their children was William d'Aubigny, 3rd Earl of Arundel. The Duke of Norfolk's Archives Assistant Librarian Sara Rodger wrote that William "did have three sons, William who succeeded him as Earl in 1196, and Alan and Geoffrey, of whom we know nothing." His daughter, Matilda d'Aubigny, married William de Warenne, 5th Earl of Surrey. In 1176/7 he was created Earl of Sussex and in 1190 he inherited the earldom of Arundel. He is buried at Wymondham Abbey, Norfolk, England.[3]
References
1.
Brown, R. Allen (1988). Castle Rising Castle. London, UK: English Heritage. p. 15. ISBN 185074159X.

Aubigny, William d' [William de Albini; known as William d'Aubigny Pincerna], first earl of Arundel (d. 1176), magnate by Graeme White, Oxford Dictionary of National Biography

http://thepeerage.com/p10676.htm#i106760

From Foundation for Medieval Genealogy: fmg.ac/Projects/MedLands/ENGLISH NOBILITY MEDIEVAL1.htm

WILLIAM (-24 Dec 1193, bur Wymondham Priory).  Robert of Torigny names "Guillermum primogenitum suum et Godefridum et…comitissam uxorem Johannis comitis Aucensis" as children of "Willermi de Albinaio quem vocant comitem de Arundel" & his wife[17].  He succeeded his father in 1176, generally known as Earl of Sussex as the castle of Arundel was retained by the crown on his father's death.  They were restored to Earl William in 27 Jun 1190, after which he was referred to as Earl of Arundel[18].  The Annals of Waverley record the death “in vigilia Natalis Domini” in 1193 of “Willelmus comes junior de Arundel”[19].  m (after 1173) as her second husband, MATILDA de Saint-Hilaire, widow of ROGER de Clare Earl of Hertford, daughter and heiress of JAMES de Saint-Hilaire & his wife Aveline ---.  Robert of Torigny records that "Willermus de Albineio…comitem d'Arundel…[filium] Guillermum de Albineio primogenito" and "relictam Rogerii comitis de Clara filiam Jacobi de Sancto Hilario"[20].  Her name is confirmed by the undated charter which records that “Wilielmus comes Sussexiæ” confirmed donations to Boxgrove Priory by his predecessors “Rogerus de Albineio, et Willelmus Pincerna…et Willielmi patris mei filii reginæ Aeliz, et Matildis matris meæ”[21].  Earl William & his wife had [two] children: 
a)         WILLIAM (-Cainell, near Rome before 30 Mar 1221[22], bur Wymondham Priory).  “Wilielmus comes Sussexiæ” confirmed donations to Boxgrove Priory by his predecessors “Rogerus de Albineio, et Willelmus Pincerna…et Willielmi patris mei filii reginæ Aeliz, et Matildis matris meæ” to Boxgrove Priory by undated charter, which names “domina Avicia, uxor Rogeri de Albineio…et filiorum suorum Willielmi et Nigelli”[23].  He succeeded his father in 1193 as Earl of Arundel. 
b)         [AGNES .  A manuscript record of the Mowbray family (many of the details in which relating to the early generations of the family are inconsistent with other sources) states that the wife of “Willihelmus…primogenitus et hæres Nigelli de Molbray” married “[filiam] comitis de Arundel…Agnetem” who was mother of his two sons[24].  The identification of this person has not yet been corroborated from other sources.  m WILLIAM de Mowbray, son of NELE de Mowbray & his wife Mabel --- (-Axholme before 25 Mar 1224, bur Neufbourg).]