Why would she ever want to do the financial stuff without a lawyer? Plus, I think that's already been settled, hasn't it? Or almost?
Look - dropping the rope is NOT about not being vigilant about your child. But it's about foiling his desire to use the child custody as a way to get AT you. Document everything (but I don't think any of the physical things that have happened so far would qualify in a judge's eyes as negligence - to be fair, stuff does just happen to kids and even good fathers do not watch them like hawks the way that most moms do. Men are risk takers - and that's good, kids need to learn to take some risks too). Still, if the pattern continues, you may end up with enough evidence. Hopefully OW will stick around to be a moderating influence.
The desired outcome is for him to stop fighting you for custody - which I think is more likely to happen if he has a taste of it and decides it's too much work for him. (Sounds like he's already decided it would interfere with his weekends, huh?). That's not going to look too good to a judge if he's been given a reasonable amount of custody time and he isn't taking it. These pages are littered with men who fought for custody time and then stopped taking it once they got it. For your ex it's just a way to push your buttons - so don't let him see they're pushed.