I completely agree. Give him an inch and he will take a mile.
Read what you've written here.
Let him go on and get sober. Just because you separate or divorce doesn't mean you can't rekindle if he proves himself. But make him prove it. Don't put yourself or your children through it.
When I separated, I heard all sorts of lovey-dovey promises. My canned answer became "If you're still sober and I'm still single in a couple years, then we'll talk." That's all I said. Over and over and over. I had to say it a few dozen times to believe it myself. But eventually, I started to believe it. Now separated for nearly 3 and divorced for 1.5 years, there is NO WAY I would go back to that hell.
And FWIW, my marriage was not abusive. (We did EIGHT years of counseling. Lot of good it did. Wouldn't recommend that path, honestly.)
Be strong, and good luck,
D