Welcome-- I'm pretty new myself.
Are you wondering about whether you want to stay with him still? How are you doing day to day? How are your kids?
Your story sounds so familiar-- hope, a period of change, sliding back into the drinking, you have kids and are worried about finances (that's been a big one for me too) and your AH just doesn't or can't care about the ways his drinking is impacting everyone else... I'm not planning to stay with my AH but when I was, I was really stressed constantly about the money he was spending on food, cigarettes, coffee and alcohol-- we couldn't afford it but he was just doing whatever he wanted without regard for the repurcusions for others...
It must be confusing and sad for your kids and you huh?