This isn’t easy for sure. And I know a part of this is not wanting to be the one to “end the marriage”
He is really a master manipulator.
He needs to get his closure and heal on his own. That isn’t for you to do. Help him and support him in this. That’s on him.
I don’t know how you trust him when he keeps lying. And getting numb to this is actually more worrisome.
I would have him leave and get this apartment and let him Heal and get over his AP of 2 years all on his own. Then if he truly heals and stops being a manipulator and liar, maybe when he’s healed you guys can work on marriage 2.0.
But he is all over the place. he is not ready for marriage 2.0. He’s got a lot of work to do on himself before he is ready to work at a better marriage.
Your kids will be fine. Probably better actually.
Time for him to get out of your space and let him work on his issues