What event chains do different Way of Life focuses unlock

King can never be a vassal of another king, and there is no “partial vassal” or something like that (and the same applies to all the other levels too).

The duchy will become part of your kingdom (de facto, this won't change which kingdom it is part of de jure). But if the crown authority in the other kingdom is high enough, you won't get the duchy (it prevents titles to pass out of the realm through inheritance).

There are three main ways to get rid of your wife:

1. Assassinate her. If this fails, your wife may be lethally annoyed at you.
2. Start a plot against her, from the Intrigue screen. This plot will always be available when you are married. Again, if your wife finds out (due to one of your fellow plotters spilling the beans), your wife may let her displeasure be known in similarly-lethal ways.
3. If you're Catholic, you can ask the Pope for a divorce. It costs 50 piety, and you'll need the Pope to like you, but otherwise it has no drawbacks; you can re-marry immediately after a divorce.