I did the exact same thing when I left, I really wanted to see him, talk to him. When you feel the need to do that, find something else and focus on that. As you say, you will be upset all over again.
When a relationship ends, it's like an open wound. You have to let it heal (no contact) because if you keep picking at the scab that forms (by caving in), then it never truly heals. As you can see by his actions concerning your kids, he is picking alcohol over you, them and everything.
What I found comforting was to surround myself with other people, family and friends. I forgot instantly about contacting him and enjoyed myself! I phoned my mum all the time just to chat, sent funny pictures to my friends and bought a load of chocolate and crisps, plonked myself in front of the TV and lost myself in films.
And now, after over two weeks of being apart, I'm not bothered. He is messaging me, and I'm not affected in the slightest. I am civil, but not friendly and not giving out any signs of reconciliation.
You are a strong amazing lady and you deserve the best. And even though you may want it with all of your heart, he is not the man to give you that. He is giving his love to the bottle. You need to give your love to yourself and your kids, and maybe if the right man comes along, you can give it him. But not to the man who can't keep a promise to his daughter, and who disrespects you and the family he has left behind.
Your daughter is right - it's his loss!