You can give ultimatums, if you are willing to see them through. You can tell her--get sober, stop sleeping around, and get your life together or I will divorce you.
That seems scary, doesn't it?
Here's the thing though--she has a choice to make, and so far she is botching it big time.
She can turn herself around, or not. Either way you win. Nothing is permanent in this life, not even divorce should she turn back into the woman you thought you married. Yes, people even remarry, as crazy as it sounds.
My point to that is this--continue doing the right thing until she turns around. If she never turns around you win. If she turns around, you win. Either way, you and the kids win--and by winning--I mean living a sane, mentally healthy and stable life...a good life...the kind they and you deserve.