Well, alcohol or coke, really doesn't matter, he is an addict. As for the affair, he is feeding you a load of bs, she just wasn't shaking his hand, I'd look a little lower. An affair that goes on for a year does not make for a casual meet and greet.
Addiction is one thing, cheating is another, to me, cheating is a deal breaker.
The only light at the end of the tunnel is for you to get healthy, recover from codependency, go to meetings and start getting your life and finances in order. Don't deposit money into any joint account you have with him. Open your own account, stop
supporting him and his addictions.
Finally, children first, they will take their childhood into adulthood, do what is right for them. They need one responsible parent, tag...your it.