Guillaume of Jumièges records that “Ricardus Turstini filius” served Duke Guillaume II loyally after his father “Turstenus cognomento Guz, Ausfridi Dani filius...præses Oximensis” rebelled and was forced to flee into exile. "…Turstinci vicecomitis…Turstinci Gazel…Richardi filii Turstinci, Roberti fratris eius…" witnessed the charter dated to [1047 or before] under which Guillaume II Duke of Normandy confirmed the donation by "Adelelmi…Beatricis uxor eius…Rotberti filius eius" to the abbey of Mont-Saint-Michel.
Vicomte d'Avranches. "…Richardi filii Torestini…" witnessed the charter dated to  under which Guillaume II Duke of Normandy donated property to the abbey of Marmoutier. "…Willelmi filii Osberti, Rotgerii de Monte Golmerii, Richardis vicecomitis Abrinchensis…" witnessed the charter dated [1055/56] under which Guillaume II Duke of Normandy "in pago…Constantino, villam…Flotomannum" to Saint-Florent de Saumur. "…Ricardus vicecomes Abrincatinus…" witnessed the charter dated 1064 under which Guillaume II Duke of Normandy settled a claim in favour of the monks of Marmoutier relating to property donated by "Guido de Valle".
The Chronique de Normandie, based on le Roman de Rou, names "Richart d’Avrenchin" among those who took part in the conquest of England in 1066. "Richardi filii Torsteingoiz" witnessed a charter of William I King of England dated 1069. "Ricardo filio Turstini Guz et Guillelmo Caritate, Fulkoque filio Gerardi Budel atque Radulfo de Ollei" are named as present in the charter dated 30 Nov 1074 under which Odo Bishop of Bayeux bought "la terre de Chernet" from "Herberto de Agnellis", with the consent of "suo domino Radulfo de Conchis".
The name of Richard’s wife is not known. She is called “Emma” in the Complete Peerage, but the primary source on which this is based has not been identified. A manuscript relating to St Werburgh’s Chester records that “Hugo Lupus filius ducis Britanniæ et nepos Gulielmi magni ex sorore” transformed the foundation into a monastery. This suggests that Hugues’s mother may have been a uterine sister of King William, and therefore daughter of Herluin de Conteville. However, no indication has been in other primary sources which supports the contention that Hugues was the son of a duke of Brittany. It is assumed therefore that both lines of his parentage have been romanticised in this document to improve his status and reputation. Another possibility is that she was related to the Grantmesnil family: Orderic Vitalis records that “Rodbertus, Unfridi filius” [Robert of Rhuddlan, son of Onfroi de Tilleul and his wife Adelise de Grantmesnil] went “cum Hugone consobrino suo, Richardi de Abrincis cognomento Goz filio” to England. If the relationship is as indicated by Orderic, from a chronological point of view Richard’s wife could have been [a] daughter of Robert de Grantmesnil & his wife Hawise. 1