Hugs to all you Moms out there.
It sounds like the schools have failed your children. Kids with more severe disabilities like the ones described here could really do better in schools designed to meet their needs aka Special ed schools. My middle child was really going of the deep end behavior wise in 5th grade and I got and independent evaluation with recommendations for a proper school. Unfortunately it got ugly and I had to hire a lawyer to get the district to pay but it was worth it. Within a year of attending a proper school, I got my “real” child back. My stress level went way down knowing my child was getting what he needed. Litigation was stressful but it was easier than watching my child fall apart. Simply said, you put your child in a safe place while you go off to battle demons.
The problem with supplemental services is: it’s only a few hour per week vs spending a majority of time unsupported. A school gives a full time wrap around environment. In a special ed school, the teachers teach there because they WANT to teach a child like yours vs seen as a nuisance by a regular school. They give appropriate homework, if any, that the child can DO so you don’t have to have a fight every evening. You may even need a boarding school if the problem has gotten too out of hand to be handled by a day school.
The key to getting private school placement is to prove the public school has failed and based on what is written here, they have. My suggestion is 3 fold, 1) look for an appropriate placement(s) that your child will thrive in, 2) quietly gather evidence, emails, school work, reports from the school to show they cannot/have not provide an appropriate education and look for a special ed lawyer or advocate to help guide you.