The OP and her boyfriend haven’t made a long term commitment. They haven’t adopted one another’s children, and the boyfriend didn’t support OP’s children while they were in school.
Well they should not be bringing a child into their set up if they are not committed long term.
But buying a house jointly is a commitment, so your argument is a bit flawed.
This boy has already had a huge upset in his life. He has lost his mother effectively, his parents are divorced, he's got autism, and now he's living with his dad's girlfriend and her adult children.
Poor kid.
IMO when kids are involved you're either a family unit and pull together or you aren't.
If someone doesn't want to share the costs of bringing up a partner's child they ought to end the relationship or live separately until the child is an adult. Plenty of couples manage that.
Anyway, the first port of call was the dad contacting the school so the OP jumped the gun and should have waited for that to play out as it seems the school are willing to find a solution.
Having worked in private schools with some SEND children I did say they would try to help.