What if a king is also a duke in a different kingdom?

I play as the King of Ireland (and Castille), and I've betrothed my male heir to the heir of a duchy and some stray counties in England. As I understand it, my daughter-in-law will rule as a duchess on her own, but their heir will rule both my kingdoms and the English lands (as they are of my dynasty).

However, the English lands are of course subjects of England. So what happens then? Will the duchy and counties be separated from England and become part of Ireland? Or will I become a vassal of England – and if so, to what extent?

Solution 1:

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).