School choice

My ex wife and I are disagreeing over school. She moved to a town about 25 miles away after the divorce while I stayed in the same town. We have 50/50 custody, and at the time of divorce, agreed that it would be bad for our daughter (4 years old currently) to start kindergarten in a public school system in one of the towns that we live in. My ex wife was originally the one that insisted, and I eventually agreed. We would ultimately try to find a private school in between.

Now, she is insisting that we put our daughter in the public school in her town. The main reason she is giving is that she cannot do pick ups and drop offs in the private school, which is about equal in distance. She also claims that our daughter will have more ability to do extra curriculars because her family can help, although I've put in a plan that would allow me to do extra pick ups and bring our daughter to her activities, even on my ex wife's days.

The logistics would be impossible for me (office is in the opposite direction), and more importantly, I am concerned that by going to school in that town, that would ultimately become her home, and my house would be her "other house" for lack of a better way to put it.

Looking for any advice possible, or any information on benefits of either. My ex-wife is threatening to take me to court if I don't agree.

"We have 50/50 custody, and at the time of divorce, agreed that it would be bad for our daughter (4 years old currently) to start kindergarten in a public school system in one of the towns that we live in."

Was this agreement documented?

It was somewhat documented, but not very strictly. As we didn't know exactly where we would end up choosing a school, it says something along the lines of "we would agree to look at school choices, including private schools." The 50/50 custody is documented in the decree.