Wow, this is a big issue with me too.
When my AH is in the drunken state, we exchange insults, dissatisfaction with the marriage, whatever. The thing is, we agree.
I'm super angry w/the situation, usually on the computer revising my ez file separation papers, with all intent to march down to the courthouse to file the next morning.
But, the next morning, everything is OK with him, all forgotten, he usually has no memory of why I'm so upset.
So, what do I do?? nothing. If we still agreed on the state of our marriage, and our mutual dissatisfaction the morning after, I could actually follow through. But all is good in his world.
I understand your dilemma because you have 4 children. It would be easier to walk away if it didn't impact their life so much. It's a tough call. The queston is....how long are we willing to live like this? Only God knows that.
PS- I've lived like this for 15 years too.