See what things look like in the morning. As the others have said, you will known when you've reached the point where you're at peace with divorce, and maybe you are at the point. You'd certainly be justified. Just make sure you make the decision in a calm moment, and not out of anger for what happened last nite.
I do think you have to consider that an alcoholic, serial adulterer is NOT what you want your daughter growing up around, and not what you need around either.
