I'm fairly certain that all generals through adoption are stuck in the family tree, since their benefactor a member of the family.
The following might be of use:
HTML Code:
<min_adoption_age uint="20"/>
<max_adoption_age uint="30"/>
Problem is I get the feeling the game doesn't actually have like a repository of adoptions it draws from, so you'll still get adoptions even if you set them both to the same number, just every adopted general would be that age, so setting both to 70 I don't think would solve it, but I guess it's worth a shot.
Not sure about the bribe_to_family_tree, I recall bribed generals entering the family tree like all others, but it's been so long since I've actually played a campaign just for gameplay I might be misremembering. A lot of those settings haven't been well documented, like, at all.
You could also try increasing fertility in the hopes of producing more legitimate heirs, since the game seems to only adopt when there's a "slot", so to speak, and it seems to base it on how many cities you have as well. A 32 province faction with only a leader gets an adoption request every turn on average from my experience.