I find it concerning and disconcerting that you put so much effort into "understanding" him through these post-incident conversations and through quasi self diagnoses rather than putting down your foot about unacceptable and abusive behaviors. He should be aware of the fact that his behavior towards you, ie, raising his voice, accusing you of abuse and threatening to call police and social services is NOT OK and something you will NEVER allow.

You are far too understanding of this very sick man's disposition. And you are trying far too hard to work on this with him by understanding all of his twisted emotions that cause him to act in abusive ways.

If it were me, I would be steering clear of him entirely and I would not be giving him any of what he needs from me. He would know 100% that I do not accept the abuse by showing him that I am not going to give him affection, attention or understanding of how he feels. I would be putting my foot down so much more, and I would be walking away from him in every way possible. I feel you are coddling him far too much, enabling him and therefore, enabling further toxic behaviors from him. When does it end?

And yes, he should 100% be able to manage 2 hours alone with the kids without you being present. He is far too needy for your attention and presence, and he is an incompetent parent.

I don't know why you even want to try at this point. I'd be giving up and walking away entirely. Especially after the last incident. I know you're "stuck", but I would be calling it quits after someone did that to me. I would NOT want to coparent with them in any way shape or form from that point onwards.