Accused by the Ex of using him as cheap babysitting

[BantyCustards]

I asked Ex to have DC an extra night. He accused me of having plans to go out and wanting cheap babysitting.

This is the man who worked overtime without even asking me if it was ok - he just assumed I was 'free' and who refused to change his work hours so I could work around him so I could financially contribute and who expected any childcare to come out of my wages.

He's that convincing in his arguments I am actually questioning my position - can I have opinions?

It sounds like he is the same person that you didn't want to be married to. He is failing to learn from experience and I would guess that implying you are dishonest and incapable is not a new thing for him. You can't rely on him or trust him or expect an equitable relationship with him.
Stick to the arrangements like glue and have absolutely nothing else to do with him. Become a robot where he is concerned.

No, it's not a new thing at all, Qwertie.

Good advice