Red you are fooling yourself, honey. He has not changed and you have a long way to go to be able to judge things wisely for your and your dd's life.
Having fucked up people in your life must, I think, throw your internal 'thermometer' of normal off very badly.
You've had a scare, your illness, it has made you feel week and that has pushed you back into a situation which you think will help.
You said "I admit part of it is because he'll be useful to have around."
Please find some alternative 'support', you know the kind that really is supportive.
"The sqirming out of therapy thing is driving me mad. I'm happy to pay for it but he won't do it."
You know he won't do it, right? So something that a few pages back was one of your rules has now become, '...he won't do it'.
Have you seen those films where people walk in quick sand,? They struggle and fight and then get more caught up, eventually they stop struggling, and they sink.
How can they possibly be helped? Do not get in the quicksand in the first place. And if you do, once out, stay out.
"I'm not stupid and know what he's trying to do." Do you?
I think he is promising a lot and delivering a very little. Sound familiar?
YOU and YOUR DAUGHTER deserve better.
Did I mention my son is adopted? His birth parents loved him, but could not prioritize his needs. Please do think about this. They were not bad people, they just could not put his needs above their own needs. Their needs for drugs and drink etc.