cally, I really feel for you... this is such a tough spot to be in. But look at it this way: he must be allowed to face the consequences of his actions. If you keep making it okay, he never will. And until he does, he will keep doing what he is doing. When you start to waffle, think of him driving while impaired with your kids in the car and draw strength from that.
Go to alanon. It will help, even if you never say a word out loud. These are people who understand your life and you'll know that as soon as you sit down in a meeting. Some meetings have child care, if that's an issue. Go. Don't wait.
Also visit this BB- www.soberrecovery.com and post your story there. The upper right corner of the page has a link that says "community." When you get to community, scroll down to "friends and family of alcoholics."
What you will learn in alanon is to detach. There are also some great detachment tips at the soberrecover link. If you keep getting into it with him, then you are the bad guy and you are what he is fighting. He can come up with all kinds of reasons that he doesn't want you to control him or ream him out or tell him what to do. That's why you must remove yourself from the conflict. Then it becomes between him and the booze. You have to get out of the ring and let him battle with himself.
This isn't about you being controlling or unreasonable-- it's about your children's safety. Getting him to leave was so hard... love has nothing to do with it. You can love him and still not want him around when he's drunk. You can love him and still refuse to let him drive your kids around. You can love him and still not want to live with him.
(I may have said some of this before... don't mean to sound like a broken record.)
Edited to add:
Remember: he will not stop drinking because you tell him to or ask him to. He will only stop drinking (or change) when the consequences to him are bad enough. You will deliver some of those consequences, but most of them he will create for himself. The battle is between him and himself. Keep this in mind: you didn't cause it, you can't control it, and you can't cure it (his drinking, that is).