I read this and thought you were someone who I know, so I'm going to respond to this as though you are them! (You aren't! Your DC are different ages!)
When he left, he made space for someone better to come along, and if you want it to happen, it will. That person will come and see you for what you are.
A strong woman who instead of buckling under pressure, you upped your game. You worked more hours, you made more money, you became wholly self reliant. You have achieved single parenthood and gained a mortgage in the hardest year that most of us have had in our lives.
That shows you to not be lazy, you could've crumbled but you used his shitty description of you (which was only him trying to make excuses for cheating by the way. Cheaters try to make you seem like the unworthy one as they can try and minimise their actions a bit. He can look in the mirror and not see himself as a man who broke up a happy home by cheating on you, the woman who's loved him and had his children)
Now, where are you? You are in a situation where you have relative freedom to enjoy your life, live by your own rules, a home of your own. Children who are yours majority of the time, who see you as the one who's working hard to clear up the mess their dad made.
You are doing amazingly. Let your ex have his relationship, neither of them will trust one another completely, she knows how they got together, and he knows she was happy to be the other woman. Its an omen they will have to live with. If he's living in her house, if that relationship falls apart, what does he really have?
The man you were happy with for years is no longer there, he is not a prize, and you are not missing anything.
Please concentrate on moving on. You sound like you're making a really good life for you and your kids...take some time to feel proud of yourself.
You're doing amazingly well. X