The problem as I see it, is that your drunken, coked-up husband committed adultery and the sober husband is the one who feels remorse (or more likely fear) for the drunken husband's actions, has promised to stay faithful to you for the rest of eternity, and to seek help for his addictions.
What is happening here is that one person (the sober one) is taking responsibility for another person's actions (the drunk one). While they reside in the same body, they are not the same people. You've seen the difference between these two people plain as day. That would be like me apologizing for an act that someone else committed and swearing that it will not happen again. I have no control over somebody else's actions. And your sober husband has no control over your drunken husband's actions.
The sober husband may well be a fabulous friend, a great person, and a great father, but the drunken, coked-up husband is not. And the drunken husband has not apologized to you for his infidelity, nor has he promised to change his behavior one bit. So, when your husband has a weak moment and gives in to his addiction, as happens frequently with addicts, that weak person--the cheater, the liar, the one who will do things that the sober husband wouldn't dream of doing is in charge again.
Until the drunken half of your husband understands and takes responsibility for his actions, this pattern will continue. This is the nature of addiction.
You have the ability to choose what you will and won't tolerate in your life. But a 2-year-old child does not. And a future newborn does not. They deserve two parents who are always there for them. Who take responsibility for their actions. And who don't choose other women, booze, and drugs over fatherhood.
It may seem like an easy decision to forgive and forget now, but alcoholism is a progressive disease. It only gets worse; never better. And if you continue to overlook the seriousness of his behavior as your children grow and as his disease progresses, a drunken man may be in charge of your minor children, and he may drive under the influence with them. If you can't make those tough decisions that will keep your children safe, then the state may step in to do it for you.
So, the decision whether to stay or to leave is, indeed, up to you. But it's important to look at the big picture and consider what might be in store for your children if you continue to overlook the seriousness of his addiction and rely on hope for change.
As one smart poster said a few years ago, "hope is not a plan."