You are deft at the art of missing the point.
The court can madate treatment. They can force a kid into the state system. If the court is amenable (and they usually are) the parents can choose a treatment facility and pay for it themselves. The court cannot specifically mandate a particular facility outside its jurisdiction.
However, if the court lets the parents put the kid into RCS, for example, the kid cannot leave without being arrested and sent to a state facility. No court can order a kid to specifically go to RCS, it's an agreement between the court and the child's legal guardian. This is a very typical outcome of court mandated treatment. Everyone who is familiar with the court system knows this.
Everything I said is factual. You just don't understand it and have no experience in this area which is obvious.