This is too complicated to give you a simple “yes or no” answer. It’s true that it is early in the school year so academics probably would not be affected by a move. But how the children would respond to being moved depends on the schools and depends on the kids’ personalities and ability to adapt to change.
If the kids’ have settled in at their current school and the teachers and curriculum seem fine, then it’s important to look at who benefits from changing them. Is it in the kids’ best interests? Or is the issue really the fight between you and their father?
Clearly, it was unwise and probably illegal for him to change their school without consulting you. It sets a bad precedent and it means that a fight between the grown-ups is being visited on the children. It may indicate that no decision is a final decision if he doesn’t like it. Then what? You shouldn’t live with that tension. Your kids will be caught between the two of you if you can’t make cooperative decisions that stick. The result is that what starts as a legal matter expands into a psychological one.
I think you need to start with a lawyer or mediator to make sure such things never happen again. If it is clear that the kids’ educations will be better served at the original school, then talk to the school guidance counselors about when and how best to make the change.
I wish you well.