Does my relative have a right to barge in when my girlfriend and I are having privacy?

No matter what the cirstances, most people will know on the door as a courtesy. However, it is their house and they can do as they please. In my house, you wouldn't have been in the same room with a girlfriend. On the flip side of that, it doesn't say much for your girlfriend either. She should have some pride. Anyway, next time spring for a hotel/motel room.