Yes, you absolutely have to centre your own child.
I don't think I'll ever be doing any more supply now, but a couple of years ago I went back to a school where I used to work as a young woman.
In one class there was a boy who had 'collected' pencils from various other classes and who sat obsessively sharpening them. (Yes, I did try to get him back on track.)
He was allowed to arrive late and leave early because he was ND. He had no support.
During the lesson, he proceeded to use the sharpened pencils as darts and to aim them at my legs. Yes, I did call for back-up. It came eventually. A depute spoke to the kid and left. The kid continued to use my legs as a dartboard.
When I spoke to the depute - someone whom I knew from a previous job - it was "Oh, he's on the spectrum."
"Yes, I understand that. So am I." [Not lying.]
I declined further work at the school. Turns out that there was a similar incident (with a different ND pupil) where a teacher was so badly hurt that the police were involved. I've no idea what the outcome of that was.
Sometimes the only answer is to vote with your feet.