Mommamia - I'm so sorry you had to go thru this. Not many things worse than a kid being AWOL. I understand your fear.
I have to say I'm a little surprised that a dual-diagnosis facility is releasing her simply because she's uncooperative and ran. I say "simply" because... well, let's face it - that's how our kids are. It certainly should not have been surprising or unexpected behavior for the staff.
Does she have a therapist/psychiatrist she's been seeing at home? Have you discussed options with them? Has her current facility discussed doing any discharge planning with you (they should)? Do they have any recommendations (again, they should)? You mentioned in another post you were looking at an alternative school - have you talked with them yet?
In the meantime, what to do? Wracking my brain here for suggestions. I think I would prepare myself for things to get worse before they get better. She's "won" in her mind here. She got what she wanted. You and husband are going to have to, in my humble opinion, batten down the hatches. If running has been, or becomes, frequent then I think you might want to talk to your local police force about their response to runaways, how soon you can call them (1 hour, 5 hours, etc.), and just kind of feel them out/familiarize them with the situation. Depending on where you live, police can sometimes be a strong ally.
If you're looking for another placement, some resources might be the guidance dept at her current school, her therapist/psychiatrist, a hospital social worker who is attached to an adolescent psychiatric unit, perhaps your state board of education (a lot of them have lists of approved residential schools, by diagnosis/condition).
My personal bias would be to look for a facility geared more toward mental health issues. Just my opinion, but I firmly believe that in my son's case, his drug use was fueled by his longstanding mental health issues. It's a chicken/egg thing, which came first, and certainly you know your daughter better than *anyone*, but ... I think that sometimes you have to address the primary issue before you can tackle the other ones. Also, while I have absolutely no firsthand experience with SA programs (because my son adamantly refused to participate), my impression is that those types of programs expect the cooperation of, and are more successful with, kids who are invested in getting clean.
Certainly any program you look at, you will need to discuss frankly their policies regarding AWOLs and uncooperative behavior. Again, I really think a dual diagnosis facility should expect that kind of behavior and have a better plan of action than simply discharging her.
I'm so sorry you're going thru this.
Edited to add: In my experience, locked facilities are extremely rare. When my son was 9 and in Residential Treatment Center (RTC), even then doors were not locked. The one Residential Treatment Center (RTC) he was in that was locked down is, I believe, the only one in the state - I can't remember how they were able to have a locked campus, but I'm thinking it was due to level of care and/or being associated with- the hospital that was next door. Rare, in any case. He was also a runner, off and on. Policy at the 2 facilities where he ran most was to contact us ASAP (within 30 minutes or so) and notify police immediately of a person "at risk" who had gone AWOL. At the first Residential Treatment Center (RTC) (when he was 9-12 years old), they would give chase if it didn't endanger staff or other kids. At his last TLP (when he was 15-18), staff would just watch him walk out the door, only giving verbal cues that he needed to stay (sigh).