I have found that I stay very low key. I say things like "I hope he has success with that." Because between you and I, it's BS. You know that.
I had to go pick up my DD from her dad's this past weekend b/c she caught him drinking w/her there. He blamed our other child who was not even present for his reason for drinking LOL. It NEVER changes. I usto go ballistic when stuff like this would happen. Now, I simply went and picked her up. I did not speak a word to him. I told her I was sorry it happened and told her I am there if and when she needs to talk. She did talk about it for a bit then carried on w/her evening. When I have huge anxiety that my child can see, she then has anxiety too. If I am calm, she is also calm. It took a long time to get there, but here we are.
One day she will be old enough, and brave enough, that she will tell him she is not coming back. Until then, she is calm and handles herself amazingly, and that is all she can do.
Big hugs. Be there for your daughter when she hurts. Stay calm. Keep the door of communication wide open. Eventually she will not believe a word that comes out of his mouth.