How do I get over the anger?

My ex is living with someone he treats far better than he ever treated me. He is having sex and talks about her family as if it is his own (and by extension my children's) and is getting his work life sorted out to be a contributing member of society whereas he was a lazy fucking asshole the entire time we were married while I worked my ass off to support our family and he told me that he felt it was unfair that I got maternity leave just for being the mother. You know what? None of that matters. None of that means that he would ever have done any of that with me. It doesn't matter why he does all this with her. I have some theories, but again, it doesn't matter.

The fact is that you were never going to be happy with this person and now you have a chance at a different life. His failure or success in any aspect of life has no bearing on your failure or success (unless he is purposefully sabotaging you). So, ignore it. It will take a while, particularly if you have to deal with him due to children, but at some point in the future, you won't care about any of it. You just have to keep reminding yourself that your life with him was not what you wanted and now you have the ability to have the life you create. There is no guarantee that the partner of your dreams will walk into it, but you can be happy with or without a partner. Get out there and start doing the stuff you've always wanted to do, but couldn't because he was holding you back.