I added my uncle twice - can I remove one?

Yes, if you added them and they have not joined. Only the person who added someone can remove them, and only while that card is still yours alone — once they join, once an accept is mid-flight, or once others depend on them, the removal is blocked and the product tells you why.

Removing deletes the card, not the person: anything already joined or shared stays. Open invites to that card are cancelled with it.