I think if you're invested in a family system, perhaps it could be more of an "organization" system than a bloodline.
I don't think there's any thing special that could be added just because it's "family", but if the origins of the game is the same as the original game, it'd make more sense for a make-shift family of orphans/devoted girls
Regarding the "family" system, I think the whole thing should be an accessory, perhaps linked in with a possible morality/law gameplay.
Bloodline would be given a bonus to reputation/leverage so that :
if they get kidnapped/raped/killed by a rival, you'd take a heavy hit on reputation
They would give bonus gain to being whored out to local law and more rep loss on being whored out
They should start out with more than regular rebel/spirit because it'd make sense that they would be more opposed to listening to you (as children do)
The whole system should feel like a "trophy", not something you use regularly for income/source of slaves
Immersion-wise, it doesn't make sense for you to be limited by morality such as monogamy or incest, but it also doesn't make sense that it'd NEED to be so complete to keep track of multiple generations.
