Hi, kach, and welcome to SR. I'm glad you found us here. I hope you can spend some time reading around the forum. Especially make sure to read the stickies at the top of the page--there is a lot of useful information as well as inspiration there.
You are concerned about how to trust your hub again, and that's a valid concern. Trust must be earned, and he has broken yours. It will take time, and trustworthy actions, not merely words, to rebuild that trust. If his drinking is at this level, it is possible he can just announce "no more" and actually make that happen; however, I don't know that it's likely.
I also have concern for your children, as he apparently has been drunk while caring for them. How old are they? What would happen if there was an emergency situation and he was seriously impaired?
Right at this moment, educating yourself about alcoholism, what it is, and what you can and can't do about it is the most important thing you can do, in my opinion. I hope you'll continue to read and post here at SR. I'd also like to suggest looking into Alanon for some face-to-face support and education as well.
Again, welcome to SR--you are among friends.