I have joint legal and physical custody with my ex. She is trying to enroll them in a school I don't consent to. Can I block their enrollment?

Generally if you both do not agree about it, you may go to mediation.
If your ex enroll the children in a school without your consent , you have right to ask the Court to resolve the problem.
Have in mind that it is your burden to prove your thesis , not your ex's burden to prove his/her choice.
P.S. Do you live in Va?