Is it possible that your confrontation of YOUR drinking problem is making her feel a little uncomfortable for not facing hers? I ask because, if she accepts that you're an alcoholic, then she has to know that you CAN'T drink, period. It sounds like you guys used to be drinking buddies, perhaps, and maybe she'd like that back. It's easier to rationalize getting "tipsy" at dinner when you're doing it with someone else.
I don't know your situation, of course, but that thought is what jumped out at me when reading your post.
Rev