Legal Question in Family Law in New York

I assume when you use the phrase "joint custody" you mean "joint legal and joint residential custody" for the purposes of this response. If your wife wishes to modify your current custody arrangement, which I assume was court ordered, she will have to show a significant change in circumstances and then that it is in the best interests of your child to change schools. It sounds from your description of her life over the past few years that she has lived nomadically and has not had much stability. I think these issues would make it hard for her to convince a court that it was in the best interests of the child to change schools, assuming she could prove some significant change in circumstances, which she must do first. In any event, you should take any legal challenge that she brings seriously and get a lawyer to guide you.

Your agreement states that your child must attend the school district where you reside. Does it also state that you have physical (residential) custody? Does your child physically reside with you the majority of the time? These details are important to advise you as to the merits of your case. You should have a consultation with an attorney and have him review your agreement to provide you with accurate advice.