I am really sorry you're in such a difficult situation, particularly with a child on a part-time timetable.
You can't make your ex do anything. He should be reasonable, reliable and putting his children's needs first but he's choosing not to. If he is unwilling to be an active co-parent, you need to find ways to make things work without him. In your situation it sounds like it willstill be almost impossible, but it will reduce the stress because you will have more control over the situation.
Put in a CMS claim. It's a lot easier than it used to be. If he's self-employed you might still get little or nothing, but at least you'll have facts. The CMS system is really unfair and it's very easy for men to dodge their responsibilities.
Have you considered applying for an EHCP for your child? You can apply as a parent. It's easier if the school are supportive. The process can take a long time and may need you to appeal etc but it's relatively straightforward and you may get better provision. You can get them for children who are high functioning and intellectually capable but struggle with mainstream school due to ASD, for example. It does rely on there being provision available in your area.
Try to find a way of working which doesn't require any input or support from your ex. He isn't reliable so factoring him in make you feel powerless. It is really hard (it may actually not be possible). So many parents of children with additional needs are left in situations which are actually not possible to manage, and made to feel guilty when actually it is the support system which is at fault. Schools are designed in ways which lots of kids just can't cope with (too big, too rigid, too complex, too noisy) but the system refuses to acknowledge it so parents are scapegoated.
I hope you are able to find a way through.