The fishing sounds right.
My STBXH has accused me of things that it turns out he is actually doing. It baffled me early on but a counselor said its a deflection device they develop to take heat off them.
Maybe your Ex is doing something like that? It becomes an art form.
And depending on your EX, the offer to "help at the house" could either be guilt or a way to have permission to be there and know what you're doing.
I, too, have both of these things and it really aches to ask STBXH any little thing, but they have to be done and he should finish what he started...some thing!
I feel the leave me alone too and ask myself why he should get to work off his guilt? He should deal with what he did, instead.
I wish I had money to pay someone to do the work, as you say, but I have to ask him for the money right now. We have gone without or just left some things broken for long periods of time, though. Usually now its him just doing something if he comes to collect DD and I have to figure out how to stop that.
I admire your strength and am searching for it.
A person is a person, no matter how small. -Dr. Suess
Perserverance and spirit have done wonders in all ages.