Yes definitely, you only need his permission or his agreement I should say for changing the schools; not primary to secondary as that would have to change anyway, but primary to primary or secondary to secondary.
So if I were you if move house first and then once your settled if you need to send him an email and ask for his agreement to change the children’s school. You never know he may co operate!
Does he own any of the house you live in, like a mesher order or anything like that?