Vanilla Diplomatic Factional Marriages Can Result in Children (Proof)

At first, the child belongs to the father's dynasty. They seem like they do not do much since they are not politicians in your court. When I declared my child as my heir, however, all of the character options became available. This leads me to believe that If you do not declare your child your heir, then they will become the faction leader of the other faction when the father dies if the child is declared the faction heir. Until you declare your child your heir, you cannot arrange a marrage for them. Since they are technically in the court of their father by default, the only way they would get a marriage would be for the AI to arrange one either within either their own faction or with another diplomatic marriage with your faction. I haven't had this happen to me since these children seem to be rare enough. Also it seems like the portrait of your child will always be one of the random portraits for your faction. Sadly, I don't think you can convert your entire ruling court to another ethnic group like you can in Attila. This isn't really a big deal unless you get personal satisfaction from smashing a faction with one of their own leading your armies. And you still can, but you have to remember which character is, which is difficult if you've picked back up a campaign after a break.