Can I make my ex send our troubled child to private school

I have a 5 year old in kindergarten, and a 4 year old about to start in the fall. The 4 year old has been in therapy
for 6 months. His therapist is pretty adamant that he will not do well in public kindergarten, and that he needs
to go somewhere where he can get some extra attention. She feels he would be doomed to fail in a public school
(and I agree) and this would only make things worse for him in the long run.
His mom refuses to acknowledge that he has any issues. I’m not asking her to pay for anything, but, I really want
my child to start preschool at Lucy Daniels Center in Cary, and go on to kindergarten there as well.
His doctor/therapist agrees that this is the best course for him. However, she refuses to allow it.
We have joint custody with 50/50 time with the kids. So, is there any legal recourse to make this happen?
Can I take her to court to allow my son to go to a private school if its in his best interests.
Thanks for you help,

Yes, you can file a motion in the cause to have the court make that determination. I would do so sooner rather than later because court calendars in Wake County fill up in the summer. I would also put it on a date when your judge is in courtroom 9B so you have some guarantee about being reached, and you can have your expert(s) ready to testify.