OMG Needtosurvive... what a self-involved, selfish piece of garbage that man is. It's all about what HE wants, just for everything to be happy happy fine fine fine, while meanwhile, he just dropped an atomic bomb on your life, and your boys' life.
Do you have a counsellor? When I was in your shoes, I was paralyzed with pain, and I so understand how that feels. But I think right now, you've got to try to put that aside and find the deepest reservoir of strength you have. This man is emotionally blackmailing your children, and that needs to stop.
1. Lawyer! ASAP!! I have a feeling things could get messy, you must be prepared.
2. Inform your STBX that his actions are unacceptable, the boys are NOT ready to meet this woman, and that meeting will happen on THEIR timeline, not his. HE destroyed the family, and is being unconscionably insensitive, causing them additional and unnecessary distress. I personally might also add, put your dick back in your pants and pull your head out of your ass. But that's just me.
3. Set boundaries. If there is anything there he might want, get it packed up. Tell him to hire someone to box it, you put it in a giant pile, and have it taken away, at his expense. He is no longer welcome at your house, and neither is she. Drop offs are by him only, at a designated meeting spot - parking lot, gas station, etc. You mean BUSINESS.
4. Any necessary communication is via email only for the time being. This involves any financial discussions, scheduling, etc. If he doesn't understand this... that's fine. He only needs to respect it. You are done explaining yourself to him. You make the rules that are best for you and the boys. If he questions anything, that's your answer.
4. We know what you're going through, we're here, but get some real life support.
It's 1000% okay if you are messy right now, you're doing an AMAZING job. Keep going. You absolutely have the strength to do this. This man... has revealed a very ugly truth about himself, and that he is not worthy of you. That will take time to deal with, and the grief. Give yourself permission to take the time you need, but never abandon yourself in this fight.
I read something that helped me during my darkest times... a singer who said he was sitting under a tree, thinking about committing suicide, and instead, he said to himself, "get up mother f*cker". Kind of crass maybe, but I told myself that again and again. Get up. Just. Get. Up. Eventually, you will rise with joy again. And I made it true. So will you.
Sending you all the strength. xx