to be clear: my position on this is that a good faith application of the court order means that the state should be doing much more to move these kids into foster care, much more quickly.
what about the issue of corporate detention facilities?
corporate run jails - whatever their flavour - are something that you really can't have in a free society, for a couple of reasons that reduces to the profit motive interfering with the public good. that is, a corporate run jail is erected on a conflict of interest. the public good is to focus as much on rehabilitation, and keep people out of jails as much as possible; the public good is to reserve these institutions for the worst offenders, and try to get everybody else out back into society as quickly as possible. but, the profit motive of a corporate jail is to keep people in as long as possible, for as trivial a thing as can be imagined.
so, you can't have a for-profit model around these things; i'll accept accusations of minarchism in my argument that prisons should be converted to hospitals rather than shut down completely, but you need to leave the state in charge of it. you can't have people profiting from this.
now, i'm not imagining that these kids are being asked to do labour while they're locked up, although i wouldn't put it past them. but, this is where the situation gets particularly problematic in the united states when it comes to private prisons. our court system has ruled (forced) prison labour unconstitutional in canada, even in the context of sending inmates out to pick up trash. but, the reason you have jim crow in the united states - and this has more to do with that than you may realize - is that you allow for slavery for the incarcerated. that is the other position i would take on this: i would support a constitutional amendment to abolish all slavery in the united states.
so,
1) more resources to more quickly move kids into foster care, even if i understand that there is a bottleneck at the end in terms of how many placements are available.
2) you need to take out the profit motive, which may reduce the number of kids being processed.
3) a constitutional amendment to ban prison labour.
https://www.vox.com/policy-and-politics/2019/6/30/20074048/democratic-2020-candidates-homestead-child-detention-facility-florida