I think I'd ask another doctor, yours seems to be a bit ambiguous about your alcohol problem. He says you're an alcoholic but you don't need to stop drinking?? What kind of advice is that? I'd also be wary of his "off antabuse day" advice as I'm pretty sure it stays in the system enough to make you sick as hell the day after taking it if you drink. I could be wrong but why chance it? I wouldn't risk getting deathly sick by drinking on antabuse. I hear it's horrible.
And no, it is NOT willpower in a tablet.