J.S.
My name is Dad On Purpose, and I'm an alcoholic.
You DID violate his trust. Your drinking DOES affect him. No apology, no words will fix that.
Your ACTION will make your amends for you. You can't talk you're way out of a problem you acted your way into.
I'd suggest an AA meeting. Maybe read the book - it's online http://www.aa.org/bigbookonline/
I guess the real question is what do YOU want to do? You have permission to drink openly, so you don't have to sneak anymore. Or do you want to stop or try moderation?
As for the coming out process, I had to tell my parents on the phone that I was an alcoholic, had my second DWI, lost my job and have to sell my house, and btw, could I move in with them while I get my sh*t together.
With friends, 50% were supportive. Those are the ones I'm still friends with to this day.
The other 50% wanted to keep me as their drinking buddy. Turns out that was the only thing keeping us friends, and that's not a very good foundation for a friendship.
But I have never regretted telling a single person. It's just part of who I am.
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I just read a couple of the other responses, and I disagree with the view that your husband is disconnected or somehow doesn't grasp the situation. He grasps it more than you know, and more than his one comment in what I'm sure was a longer conversation (over many years) might hint at.
We (our people) only think we're doing this in private and not affecting anyone. He may not have been the best sober support person, but your drinking is not in his control.
I would imagine that if Mrs. On Purpose was found sneaking drinks, I would likewise point out that it's out of my control. Your husband sounds very sad, and very confused about how best to handle this. Should he say your drinking ruined a good relationship? Should he ignore it and look to tomorrow? Should he yell?
I imagine if I were in his shoes, keeping it together would be my first priority. :)