If I'm the King of England and my wife has a claim on a duchy in Scotland, would pressing her claim make her my vassal?
Only if she's already a duke in your realm., otherwise, she'll be independent
if the character is already your vassal, they will remain your vassal, UNLESS the title you win for them is the same rank as your highest title. I BELIEVE that, if they are of your dynasty, they will become your vassal when you press their claim. otherwise, they become independent.