My kitten is submissive to me, but likes to get her claws into others.

I don't see anything wrong with this, it's simply another aspect of her personality she wants to explore. That she does this with others doesn't bother me, because as I told the owner of the local dungeon: "We're here for her, because she sure as hell isn't going to get to do that at home."

Some people are purely dominant, others purely submissive; if you want to explore both worlds ... well, enjoy yourself.