And the merry go around of denial continues.
What stopped you from leaving before?. Fear of him, a fear of being alone, financial reasons?. What are the reasons?. If you can articulate your fears more then perhaps these can be broken down into more manageable chunks.
He has already broken this family because of his alcoholism and he is saying all the things that alcoholics say. Its never their fault and you're stopping him from having his "fun".
Better to be from a so called "broken home" too than to remain in one for what are really your own reasons. Did you yourself grow up seeing a heavily drinking parent too?.
What are you getting out of this relationship now?. What needs of yours is he still meeting?. I have to look at you as well here Tulip because you're as much caught up in his alcoholism as he is and your kids are being dragged into this too. Its no legacy to leave them and its no nice childhood for them either. What do you think they are going to remember the most about their childhoods?. Have a look at websites detailing how children are emotionally affected by an alcoholic parent; that should remove any scales from your eyes. Like many posts of this type too its mainly about the alcoholic.
Hard as this is to read I would urge you to read this article:-
www.soberrecovery.com/forums/friends-family-alcoholics/68440-alcoholism-tragic-three-act-play-there-least-4-characters-1-a.html
You cannot and should not use the children here as a reason to stay with him. What do you want to teach them about relationships and what are they learning here from you two?. They are already learning really damaging lessons here by thinking their father is more "fun" when he is drunk, this is terrible. They could all too easily themselves end up with alcoholics as partners and they are probably already alternating between tiptoeing around dad and laughing along with him. They are becoming super responsible and learning to be codependent too like you are. By being with him also you are propping him up and otherwise enabling him, this state gives you a false sense of control. You have NO control here over this and he has to be the one who decides to seek help. If he does so because or for you it will fail.
His alcoholism is and remains the elephant in the room. You are merely firefighting this whilst you lurch from one crisis to another. This will not end until you finally decide that enough is enough and give your own self permission to leave him. There are NO guarantees here re alcoholism; he could go onto lose everything and everyone around him and he could still choose to drink afterwards.
Abuse like this thrives on secrecy and if you really cannot open up more to family and or friends then I would urge you to contact Al-anon and keep posting here on your thread. You need a safe outlet.