When they fight, does one side leave my country? How can I find out? Or is it just the duke that I don't side with will leave once I declare war?
Can I just let them fight it out and then they will both will stay with me once they are done fighting? What happens to titles then?
If you join in, during the Peace process, you might have failed to stipulate that the losing Duke will once again become your Vassal. Once you join in the fighting, you in essence have declared war on that vassal and at that point, he is no longer part of your Realm.
What happens if you let them fight it out, depends on what claims each has on the other. As long as you don't get involved and they finally settle peace, no matter who wins/loses, they both stay in your Realm. If one side gets wiped out, and the other side doesn't have claims on the Duke title (for example), you'll get to re-create that Duke title (as long as you have 2/3's of the lands that comprise that title in your Realm).
I usually check who has claims on the other. If I don't wish either Duke to grow more powerful, then I'll go in and settle for peace in terms that benefit ME. Those opportunities are nice to have, as that is when I get to re-apportion Titles that have gotten messed up due to inheritance/sub-vassals leaving their Dukes/whatever. Or an opportunity for me to snatch up a juicy County for my own Demesne.
