Please call your local child care licensing agency and ask them about special needs child care. In Oklahoma all the better child care centers get certified and they have more training and be better able to help your child with things.
I can't say they'll take kids and pick up kids from your school or that it will work out but I do think there might be an option you haven't found yet.
Why can't a family member or friend come and stay with her for an hour each morning and have the bus? drop her off at that person's house?
We have done this. The mom worked 5 days on and 5 days off. She brought her tween son over on her way to work in the group home she managed and he stayed with us until she got off a few days later.
She was off work during the days while the residents of that house were at work. She was also off the clock during the nighttime hours but her son was not allowed to stay with her so even though she was off work during the night he couldn't stay with her.
His bus picked him up and dropped him off at our house those days then took him to and from home on the other days. It worked out very well. She only paid us a little bit each day. He wasn't any trouble and a real sweetheart.
I think that having to quite work and lose your insurance is a drastic step to take. I am sure you aren't doing it without much consideration and care for your family.
Please find out if there is anywhere at all where your child can be dropped off for child care then go to school and then get picked up and taken back to the center. That's about the only way this will work of course.