You have two options.
1) You talk to the mother of your children to reach an agreement.
2) You get a judge's order.
Obviously the first option has big advantages. First of all it avoids you and her each giving money to lawyers. Second, it is nicer for you to not have to fight all of the time. And third it is better for the children.
How important is this to you? Have you listened to her reasons for choosing this school? Is there something that she could give in on to make you be able to accept this decision (or vice versa).
If this were important to me, and I felt I tried my hardest to work this out with my ex-wife, I would pay to see a lawyer (generally the free consultations are worthless sales pitches). Once I got a lawyer's opinion, I would relay it to my ex-wife and then hope that I wouldn't get into the ugly mess of a legal fight.
Better to try to reasonable.