Just remember, everything you hear about her through him could be a lie. She could be making up a lot of stuff just to get her way with him. He's relaying her situation to you -- BUT how would either of you possibly know what's actually going on? BIG RED FLAG, I'd say.
I would tell your BF in no uncertain terms that if she moves in with him, you know it would severely hamper your time with him, may put an end to something really good you have together, and place a huge burden of responsibility on HIM to be in the role of caretaker-father-provider. I would also ask him if all the drama and headaches she gives him are worth jeopardizing your relationship.
You have very nicely and generously offered to be helpful and understanding enough; I think now it's time to be a little hard-ass and stand firm on what you will and will not accept. If you're not sure what you are willing to accept, figure it out and don't feel obligated to be nice. Ask yourself what you need and then ask him for that. From there, you can negotiate, but don't concede anything until you've stated what your ideal is.