Rodolf was the son of Eperleng, a rich owner of several mills at Vaudreuil, and of his wife Sprota, who by William I, Duke of Normandy had been mother of Richard I of Normandy, making Rodolf the Duke's half-brother.
According to William of Jumièges, Rudolf had to quell dual rebellions in 996, of peasants and nobility; against the former he cut off feet and hands. He arrested the chief aristocratic rebel Guillaume, comté d'Hiémois.
The counts of the duchy of Normandy were in place from around the year 1000; Rodulf is the first whose title can be attested by a document (of 1011). Pierre Bauduin following David Bates states that territorial designations for these titles came in only in the 1040s. Contemporary sources, and Dudon de Saint-Quentin, speak only of Rodulf as "count", never "of Ivry"; this is found only in later writers. Ordericus Vitalis, for example, calls him count of Bayeux. Historians now consider this erroneous, following the later Robert de Torigni, who makes Rodulf, the comte d'Ivry.
In strategic terms, Ivry was on the boundary of the duchy of Normandy, by an important crossroads on a Roman road, by the valley of the river Eure. Over some decades the Normans had struggled there against the forces of the county of Blois, after its control had reached Dreux. This position mattered for the assertion of domination of the south-east of the Évrecin. Consistently, the duchy may have conceded to the county in the direction of the county of Hiémois and towards Lieuvin (forêt du Vièvre).
His children by Eremburga:
- Hugh, bishop of Bayeux (c. 1011–1049)
- Emma, who married Osbern the Steward and was mother of William FitzOsbern
- Daughter of unknown name, who married Richard de Beaufou
His child from Albreda is:
- Eleanor Searle, Predatory Kinship and the Creation of Norman Power, 840-1066 (University of California Press, Berkeley, 1988), p. 292 n. 8
- Francois Neveux. A Brief History of The Normans (Constable and Robinson, London, 2008), p. 74
- Eleanor Searle, Predatory Kinship and the Creation of Norman Power, 840-1066 (University of California Press, Berkeley, 1988), p. 108
- The Normans in Europe, ed. & trans. Elisabeth van Houts (Manchester University Press, 2000), p. 57
- François Neveux, La Normandie des ducs aux rois, Ouest-France, Rennes, 1998, p.65
- Guillaume de Jumièges, Histoire des ducs de Normandie, éd. Guizot, 1826, interpolating Robert de Torigni and Ordericus Vitalis, p.111-114
- David C. Douglas, 'The Earliest Norman Counts', The English Historical Review, Vol. 61, No. 240 (May, 1946), p. 131
- David Bates, Normandy before 1066, p.114
- Pierre Bauduin, La première Normandie (Xeme-XIeme siècles), Presses Universitaires de Caen, 2004, p. 200
- Pitte, Dominique (2000). Le Château d'Ivry (Eure)- La Normandie vers l'an mil. Rouen: société de l'histoire normande.
- Gazeau, Véronique. Le patrimoine d’Hugues de Bayeux (c. 1011-1049). pp. 139–147.
- Detlev Schwennicke, Europäische Stammtafeln: Stammtafeln zur Geschichte der Europäischen Staaten, Neue folge, Band III Teilband 4, Das Feudale Frankreich und Sien Einfluss auf des Mittelalters (Marburg, Germany: Verlag von J. A. Stargardt, 1989) Tafel 694A