Your story resonates with me a bit. I can only imagine the euphoria you felt when he sat with you and the kids and said "no more". Then came the heartbreak of realizing it was only something he said.
Last week after a terrible night I said no more. He agreed. No more. The next day he said....."it will be a long time before I ever drink again" (rationalization begins)......the next day I smelled it on him.
Last night I found him obliterated. Its been a week since he said "never again". Without active recovery any promise to quit is nothing more than words. My AH was sober 10 years but the last 5, and the 2 that I have been with him, he has been a dry drunk. Sober yet not working a program therefore relapse has been a part of our relationship I didn't know because before SR I really didn't know what alcoholism is.
Would you believe that in my mind when I thought about what would need to be done if he ever relapsed - I thought that he may go on a binge and then come to me immediately and say I need to go back to AA, or that I would say "We must go to AA" and hand in hand we would go. Uh......not so much.
I am so sorry for you and your children, I am single....and it has been overwhelming trying to figure out how to handle it. I am getting there, you will too. Sending prayers.