Last question first - no, AA can't help with this. But, if you are in the sitaution you describe, probably no one can help with this and you are probably asking the impossible. If it is ruining your family's (and your) life and you still carry on doing it, it is not likely that willpower or a tablet are going to sort this out for you.
I'm not at all surprised that you don't want to give up alcohol - I felt the same. After all, if this is your life WITH a drink, how shit is it going to be WITHOUT a drink, right?
I am pleased to say that, having come out the other side, life is loads happier and more fun and just plain EASIER without a drink. You could not pay me to go back to drinking and that is a fact.
As to what AA is or isn't - I can guarantee you that no one will "make" you abstain. There isn't really a plan B, but if you want to keep drinking, then do so - AA won't make you do anything. It is true that "the only requirement for membership is a desire to stop drinking" but, if I'm honest, i didn't even have that. I just had a desire to stop drinking the way I was drinking.
As for not admitting things in public, you do not have to speak at an AA meeting and, even if you do decide to speak, it's hardly public - it's a group of people who are all there for exactly the same reason as you. There are no leaders, no therapists, no one in charge. And it's called "anonymous" for a reason.
May be worth giving it a go ... Unless you have a better idea?