Someone pointed out that existing laws already prohibit a lot of the abuse that goes on in these places, and that the laws are simply not enforced. I'm not sure that's really true. The courts' interpretation of the 14th amendment gives parents a lot of leeway in making educational and health care decisions for their minor children.
That's step one -- exposing these places on the issues of education and health care. If the education is sub-standard or non-existent, how can they call themselves "schools?" If there is no evidence of following established mental health care practices, including assessment of progress by state-regulated practitioners, then they are not "therapeutic" either. This will need to be done on a facility by facility basis.
Once a facility loses its facade of being either a school or a therapeutic center, it will be left with no label other than "privately owned detention facility." And THAT is something I doubt would withstand current interpretations of parental 14th amendment rights. In that event, any advocate, including the state, would have cause for removing a minor from unlawful incarceration without due process.
BTW, I think the educational angle is the more productive avenue of attack. Many public school districts subsidize all or part of the fees these places charge, as a result of a couple different laws (like IDEA) and the typical school district's inability to provide a suitable education alternative for children with these types of 'special needs.' If the teen gulag "school' looks too much like a residential treatment facility, the public school district will say it's a health care facility and the parents' health insurance must foot the bill (which they won't, because they aren't stupid and they know this isn't really 'health care').
So it's a fine balancing act between presenting a "therapeutic" face to the parents, while simultaneously presenting an "educational" face to the public school district.
If you can eliminate the public school systems (our tax dollars!) paying for kids to be incarcerated, and force the entire bill on the parents, at least the number of kids being sent away will be reduced, until such time as these private detention facilities can be shut down for unlawful incarceration.