Hi Brownsugar and welcome! Glad you found us.
First and foremost, please know that none of us are doctors or experts.
We're parents who are traveling a similar road as you and we bring a wide variety of opinions and experiences. We also bring our biases based on our own experiences - so take what info you can use and don't worry about the rest.
The first thing that really leapt out at me was the medications that your son is on. Just based on life with- my bipolar son, I'm wondering why he isn't on a mood stabilizer. Abilify is usually used as an add-on medication. Stimulants can be a very iffy proposition in bipolar kids, sometimes actually promoting manic behaviors (and "manic" in my kid was always extreme irritability that led to violence, not an elevated mood). Has he ever been on a mood stabilizer (Tegretol, Depakote, Lithium)?
How is his mood? It is pretty much the same or does he go up and down? If it does change, how often (minute to minute, hourly, daily, or longer)?
Does he have an IEP in school? You say he's having problems there - is it mainly behavioral or does he have academic problems too? I know, sometimes it's hard to separate the 2.
Has the school done formal testing to rule out learning disabilities? Do you know much about his birth family, in terms of history of mental illness and possible exposure to drugs/alcohol prenatally?
Have you talked to his psychiatrist and therapist about residential placement? Is it something they're recommending? If not, what are they recommending? Are community-based supports available to you - respite, mentoring, wrap-around services?
Sorry, I know, a lot of questions. It helps to know what you've tried and what resources are available, both in the school and community. As far as finding residential placements, the resources I'd start with are psychiatrist and therapist, as well as your state dept of mental health. A person who was extremely helpful to us was my son's therapist at the hospital where he was admitted on a regular basis. She was aware of funding sources and had excellent insight into which programs might be a fit for our son and which ones we wanted to stay away from.
Again, welcome and I'm so glad you found us!