That's why I did say "a bit on the ASB side..." in my o.p.
@FillyofDelphi
Though to limit the level of Papal suspicion it could be only a father to heir sort of thing possibly being seem as a rather harmless tradition though Rome has been known to be a bit over the top. As I know nothing about education of the gentry during that (and most periods to be frank) maybe the secrets could be entrusted more to their daughters as the church seems to be worried about raising strong catholic men and all that.
As a rule, the Church was pretty much the only organization that could provide a quality education during the 10th century, and as a noble you'd be expected to have your sons tutored. As for the father to heir training, that'd be pretty hard with all the responsibilities of managing a realm (plus, the Normans had to be quality warriors as well which is a time consuming process; after all, the purpose of giving them Normandy was so they would defend Ile-de-France and the core of West Francia's river system from OTHER viking raiders), so baring a rather unique set of circumstances you're either going to have Catholic sons, or ones who have some kind of syncratic faith which will have the lid blown off of it at some point. As for entrusting it to their daughters, CULTURALLY that would make sense between the two given the (relative) degree of independence and more equitable (not EQUAL, per say; you still had women's and men's work, but in terms of levels of respect and authority) social expectations of the genders... for the fathers. Since their sons are being raised with and expected to act along more traditional Christian morals, however, they'll not take too kindly to their sisters being so uppity. If for no other reason than it "ruins" them for potential husbands of a similar rank from the rest of Frankish high society.
Fundimentally, you need the Normans to be in contact with their "roots" in the broader Norse culture for them to stave off assimilation. Given they aren't likely to get it domestically from either their subjects or social peers in the Frankish nobility... perhaps greater survivability of Pagan Norse nobility and traders in other realms who could provide them with religious companionship? Have Norse York, Dublin, Norway, ect. become big trading powers in the North Sea, with the Norman cultural uniqueness more tolerated by the French as it gives them a role as "gatekeeper" between the Pagan Norse and Catholic Continental worlds in a way that's socially tolerable to them both, in a manner similar to the Italian traders in the Middle East existing on the edge of the broader European Feudal system?