From what I've read of your previous threads, I think she's driven you to breaking point. And I don't think she's your top prioity at all - your family is and she's made it clear she doesn't want to be part of it. If she wants to go, let her go.

I disagree with paying her board AT ALL. She has a home. If she doesn't like it, then she can act like an adult and pay her own way. If she comes to an agreement with her friend's mum, then that's up to her. This may sounds cynical, but if you go 70/30 with her, then expect that your 30% will be paid, the 70% won't and then you'll be pressured to pay the rest. Of course it's good you're involved in discussing things with her friend's mum, but DO NOT agree to comitting money to anything. She's shown she'll abuse the situation if allowed to. She can get a job if she wants to be independent.

It almost seems predictable that she'll soon wear out her welcome at the new place and have to find something else. On the other hand, maybe seeing how other people live will teach her some respect. Either way, it probably best for the rest of you if she's not around anymore. From that I mean, you can regroup, live without the stress and hopefully develop a better relationship.

Personally, I think you've been bending over backwards for her and it's enough.