There must be more to this as it is strange the court would allow a child to be on limbo. Is it perhaps that you all agreed to joint custody yet you continuously disagree and are running to court. You need to sit down with your attorney.
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Are you and his father divorced? If so, take a look at your divorce papers if you have them. There is often a provision stating which parent holds the final decision making authority for medical, religious, and educational matters in the event that both parents can't agree.
Without reading the actual custody order, it is difficult to comment on whether or not you would violated the order if you decide to change schools. If you were to enroll your son in the new school, and the other parent filed an action in family court challenging this decision, the judge will be mostly interested in the following factors when making his or her determination: Does the child primarily reside with you most of the time? Are there any court orders that already set forth your child's education plan or outline the parents' authority for educational decision making? Is there any provision in any of your court documents regarding what happens if the parents do not agree? Does the new school involve relocating your child to where visits with the other parent would be interrupted? AND most importantly, would enrollment in this new school be in the best interest of your child? You should discuss your specific facts in regard to each of these questions with an attorney who can assist you with your decision and advise you on the probability of family court ramifications.
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Even though you both share legal and physical custody it is usual for one parent to be designated the "residential" parent. That is the parent responsible for getting the child enrolled in school and the basis for deciding on the school district that the child will attent.
This advice is not meant to create an attorney-client relationship and is a general anwer to the question posed.