I'm not sure what is meant by "a full assessment", but she did have at least a PTSD assessment done at her TBS by her therapist who had worked a good bit with domestic violence. He told us that she did meet criteria for PTSD. Unfortunately, he left the program 2 months after my daughter arrived.
I looked at www.austinriggs.org. Frankly, this option scares the hell out of me. Maybe I'm in complete denial, but I just can't believe she needs a full-blown psychiatric facility.
It sounds like your daughter has been assessed by licensed professionals. The only other question I would ask (and it sounds like it has already come up) is what they would recommend for treatment. Again, I don't know the case, but it is very possible that they will recommend outpatient treatment. I have worked with multiple battered women in outpatient therapy. It took years for any of them to be able to really break ties with their abuser -- sometimes out of a very real fear of being killed -- but more often because they could not leave the relationship. The possibility of leaving was more terrifying than staying with a partner who beat them.
There is a harm reduction model to therapy that I use with people who find it impossible to keep themselves safe (whether from a partner, strangers, or themselves in the case of extreme eating disorders or with people who cut or burn themselves). In the cases of the women with whom I've worked, the therapies do not go after trying to make the woman leave their abuser (at least directly). Rather it focuses on how the woman can survive in the relationship (and plan for the nights when she needs to escape) until leaving is a real option for her. By taking this tack we can keep the therapy relationship alive until she is capable/ready/willing to keep herself safe.
Re: a psychiatric facility. Don't let the name scare you off. What it means that they have multiple agency oversight -- a good thing in my mind. Many "therapeutic boarding schools" are now also registered hospitals. If you are able to get insurance to cover part of the tuition you can be sure that they are recognized as an inpatient treatment facility. Ask around -- it is more common than you expect.
The thing about Riggs is that they have an extraordinary 1 on 1 therapy program with a very high staff to student ratio. They would have an intake with your daughter and decide whether placement would be indicated.