All I can say is I think Gypsy's words are excellent and right to the point.
Work on you. Stop everything that is about him. He has to clean up his own house. It is no longer your responsibility.
Your "falling" for his remorse is natural, but again, he is all talk and no action. When his action meets his talk, then you can consider interacting w/him again.
For now, let him deal w/his own pain and you concentrate on yourself, your children and your family.
STBX has made his bed and now he needs to lie in it. He was trying to "get away w/it" w/out being caught. He blamed and accused you and said you were to be blame for your marital problems. He "gaslighted" you into thinking you were the problem and not him.
He's a master manipulator who has been exposed. Now it is his turn to sit and take the beating he deserves.