Take this advice. Adopt the law that makes the strongest son inherit, so that you can in effect appoint your inheritor by giving him titles and land, to make him the strongest militarily. This can guarantee your inbred bastard with 1 in each stat, whom seems to have an unnaturally long life span, never gets on the throne.
Second, as far as Bad Boy goes, the best way to deal with it, honestly, is to not take shit that isn't yours. Unless it belongs to a Muslim. Or a Pagan. If you are the King of a Large Kingdom, when your son takes the throne, it is likely that several vassals will try to rebel. The tactic here is to offer them peace recognizing them as the rightful holder of their titles, and demanding that they return to a state of vassalage under you. This, for me, almost always worked, usually without much of a fight, if any.
The reason they try to Rebel is, A: The son of the King inherited the King's claims to all the titles he granted to his vassals. Titles he got through brutal badboy inducing warfare. B: The New King has relatively high badboy, and is therefore likely to try to enforce his claims by warfare.
Theoretically, their goals are simply to have their hereditary titles recognized, and do not trust you to have such respect for them. With this knowledge, holding together large empires is very possible. However, the other issue that will come up, if you're using DVIP, is diplomatic vassalization. Almost never do this unless the current title holder is of the same culture as you, other wise he gets a higher possibility of trying to break away from your rule.
Finally, the best place to start, in my opinion, is Cyprus. Plenty of Muslim provinces to expand into nearby, and the Seljuks don't start with claims on the territory, like they do with the rest of the Byzantine Empire's eastern half. However, it is probably best to wait until AFTER the Byzantine empire crumbles and the Seljuk empire fractures before making the attempt to expand. They are a bit out of your league.