Hi garden-sky
I went through something very similiar to what you are currently going through with my own udd when she was a teenager. Udd was so desperate to move out that she stayed over at many of her school friends houses, meanwhile I had the police out looking for her. Never once did any of these school friends parents contact me to say that udd was staying there. Even a good friend of mine at the time took her in for a while and even gave her ground rules for living there which I only discovered months later! It totally suprised me that I was never contacted but then again udd was so believable in her lies about me that they all probably thought that they would be sending her home to a monster who did nothing but abuse her. When she did eventually return home it was always because these friends houses werent good enough for her......she had to sleep on the sofa, ....there wasnt enough food, or there was no hot water left by the time it came for her to have a shower.

Like your dd, my udd became close to a teacher and spoke about her a lot. By that time I knew what udd was trying to do and spoke to the teacher about udd and her homelife and put the record straight. I also spoke to udd and told her that I had spoken to the teacher and under no circumstance was she going to live with her.
In the end I had to get SS/CPS involved to try to keep my udd home and safe. After leaving school she went to live with several family members which ultimately didnt work out either but at least I knew where she was and that she was safe.
Does your dd have any family or relatives she could stay with for a little while instead of this family? I think a little respite for both of you would probably work better than whole or nothing moving out stuff. The key is to keep all communication with this family open if she does decides to move out but I wonder if they really know what they are letting themselves in for? They already have their hands full with young children so how do they imagine it will be with your dd who is currently unwell. For me main my main usually after the fact was that I didnt know where she was .. I didnt know anything about this family or who lived there...or who else came and went from these homes. I was trying to keep my udd safe but she couldnt see it through her illness. You and this family need to be able to communicate and be working together if this is going to have any chance of working so I if it were me I would contact them and ask to meet up. I would also inform your udd that you have arranged a meeting and invite her along. That way your dd will not be able to manipulate anyone.