Hi Tangled,
I agree with everybody here. Forgiveness is only a path. There are many others too. Forgiveness, or any other path you may choose, is a process.
Please note that what I'm gonna say is my opinion, and only an opinion, and I might be mistaken. There are 3 things you said that make me think that you have a lot to do in this process before even getting to the point of contemplation forgiving him.
You said you wanted to be happy for you and your DD. You have every right to be happy, and you deserve happiness. However, you have to keep in mind that your happiness is in your hands, and your hands only. Nobody will make you happy, you have to make yourself happy. It doesn't mean that other people's actions won't have an effect on you, some will have a negative effect on your happiness, others a positive one. But it's still your happiness. You are the only one in control of your life and your actions, and by extension your happiness. I know, it's easier said then done. I still have to remind myself of this daily.
You also said that your AH has a smug look on his face and that you feel he pities you. Here's my question for you: Do you pity yourself? What you feel he thinks of you is not important. What's important is what you think of yourself. There's no point in even thinking of forgiveness is you pity yourself. IMO, pity is one of those feelings that strip us of our power. I personally would work on that, and on forgiving myself first.
Correct me if I'm wrong, but I also sense that your are still angry with him. I'm not saying your anger isn't justified, because it is. And anyway, I would be an hypocrite for saying it isn't as I am presently a ball of anger and rage! However, I don't think forgiveness is possible before you've shed all that anger.
Forgiveness is the very last step in the process.
One last thing I'd like to add to my novel-lenght response. You said you and your AH were separated. That you asked him last year to move out. And since then, his drinking hasn't got better and that he's even living with another woman. I'm guessing that this wasn't what you had in mind when you separated? It's none of my business, and you don't have to answer, but why are you still married to him? Clearly, his actions are not showing you that he wants to quit drinking and work on the marriage. You said you wanted and needed to move on, but I don't see how you can do this as the situation seems to keep you in limbo.
I hope you don't take my response the wrong way and that I didn't offend you, as it is not my intent. What you are going through is though, but you are on the right path. Keep working, keep concentrating on you. It will get better!
Hugs