Good advice, Susie. I also want to suggest for future reference - when you are nagged into bringing her home, make sure that the doctor saying she is OK will put this in writing, in detail, including the statement, "I am firmly convinced she is not a risk to her parents or her siblings, I realise her parents believe she is a risk but I have assured them this is not the case. We therefore will take full responsibility if any family member is harmed by the patient." Tell the hospital that if the doctor will write this, you will happily take her home.
I'm betting the doctor won't write this.
The doctor wants to send her home because he is being pressured by the hospital and by insurance. Money. It's distressing that his concerns about money (and the people pressuring him about it) are greater than concerns about your safety. But there it is - the money thing is a definite, the risk to you guys is not yet real, it's only hypothetical, a possibility only. And if you can do for her what they do at the hospital, it shouldn't happen (yeah, right - as if you could).
So you have to push the doctor's buttons harder. If he is asked to confirm his stated opinion, that she is fine and not a danger, then he is being asked to personally guarantee your safety with an attached risk of being sued if he gets it wrong. So here, he is now weighing up the money pressure from the hospital and insurance, with the risk of being personally sued if he made a wrong call.
You should be getting an attorney at this point anyway - ask about the wording of this, so you can get it right. You might find it speeds things up dramatically. A desperate doctor who is caught between a rock and a hard place is far more likely to make a placement magically materialise, than a doctor who has successfully sent the problem home (to become Someone Else's Problem). Make sure it stays this doctor's problem permanently.
Marg