You have done nothing wrong.
He wanted to come back and work things out with me but now feels stuck to be with her because of the baby and because he's afraid I'll be dishonest with him again
Has he told you the last bit, about being afraid of your dishonesty? OP you need to believe us - he is LYING to you. He is lying. You have not been dishonest. He knows that you have not been dishonest. If it weren't this, it would be something else - talking to a work colleague too much, looking at the guy behind the counter at the shop too long, mentioning a friend's husband one too many times. He decided to walk out on his children and is trying to make it your fault. It isn't your fault. You've done nothing wrong. I actually don't think getting in touch would have been wrong either.
I personally would be amazed if he hadn't been cheating with this woman, or at least talking to her. Who meets a woman 15 years younger in a matter of weeks and starts dating them unless they've already got reason to think that particular woman will date them? But ok, say he wasn't. It was still his choice to just walk out. He knows he's the bad guy, he knows that he's breaking the kids' hearts, and he's trying to pin it on you. Don't fall for it!! and whatever you do, do not get back with him.
I know you're heartbroken right now, and sad for your children. It will get better. The best revenge is a life well lived. Make yourself a lovely safe loving home with your children, a home where you're not always in fear that your small innocent actions will be dragged up years down the line as an excuse to leave you. Your children have you as their anchor and safe harbour, you can be the stability that they need. Yes, the new baby will be hard. All you can do is be generic and positive about it, show no upset, make them feel loved. When they're old enough they will see their dad for what he is, and will see that they owe their happy loving childhood to you and to your strength in pulling through this for them.