L.H.
I’m sure you realize this is a character issue. Lying and cheating are character flaws. To expect him to come clean is polar opposite of his character and you probably have a better chance of winning the lottery than that ever happening. He would have to accept responsibility for his behavior.
The more pressing issue at hand is how much He is still affecting you. I know betrayal is a very hard thing to deal with. I encourage you to seek help to process all of it. You’re carrying a lot of junk and you’re going to be involved to some degree with him for a long time because of two children you have together.
Carrying this hostility isn’t good. Sometimes you have to forgive people when they don’t ask for it or deserve it so you can move on. Please consider the toll this is taking on you and your kids.