Look at this in perspective.
What's going to have the worst impact on your child?
No enrolment, no education and a risk of more court proceedings and more conflict between his parents?
Or enrolment and education at a school that might not be your preference, but ensures there's no conflict and no more court proceedings for you, the child or the father?
I would suggest agreeing, conditional on agreement that if the child struggles at the school, then you both re-visit the matter after he's been there for a year or two.