I never got the impression that the Joker wanted to marry Batgirl. He was trying to torment her with her mother's severed ring finger. He was using the marriage bit as a joke, you know, because he's the Joker.
Well, sure, he wants to torment her but I also think he wants to marry her. Not out of love or anything like that, obviously, but for whatever his greater goal is in all of this.