Maybe it's not an "either/or", maybe it can be a "both/and" -
What I mean is, maybe you could go ahead and divorce him and move on with your life and while you're doing that he can decide if he is serious about recovery. It doesn't sound like you have a new person waiting to marry in the next 10 minutes, so he has time to get sober and SHOW YOU that he is serious.
That way, if he's serious, no harm no foul (divorces take a very long time and you can alway re-marry him a second time) and if he's not, no time wasted.
Of course for me, the three week binge would have been enough! Oh, and one other thing to consider. I read somewhere that kids do fine with a single parent family, however, it's the chaos, strife and stress before a breakup that is hard on them. A clean break might save you some money in therapy for the kids later...
Prayers you find the right answer for you.
Best of luck!