Personally I think buying the house and having them live with you is a bad idea.
It's not going to work. As has been pointed out, even if she doesn't end up with this guy, she will probably want a relationship in the future.
So playing that out, she wants to go on a date. Who will babysit? Are you comfortable with her hiring a babysitter and having the babysitter sitting with you there on Friday nights? Say she does get back together with this guy, what are the rules, can she not invite him over for lunch?
It will be her home too and she has to have that freedom.
I can't see how it will work for you at all.
I would buy a house for myself and she can rent your studio perhaps.
You mentioned you are helping her financially, I gather that is with rent, so you are already supporting him since he's living there - terrible situation, i'm sorry you are in it. I would be getting her name on any rental waiting list available, including shared accommodation and perhaps subsidized due to her disability.