Without seeing the order it is difficult to give you an answer. In most cases where one parent has residential custody with a specific visitation schedule to the other parent, the non-custodial parent cannot take the child without the agreement or consent of the custodial parent. Show your order to a local family law attorney and discuss the issues with him.
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Agree with Mr, Weinreich. The answer is no, so long as the visitation order is clear as to the schedule. If the violations or threats continue, you can bring a violation/enforcement petition in Family Court. I would consult with a family law attorney in your county; you can use the search function on this site to find one.
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First, I agree you should bring the full agreement/order into an experienced attorney to review. Second, if you are in disagreement with her doing this, then you need to capture it in writing to her so she cannot later say in court that you "went along with it." Third, perhaps you need to speak with the attorney about doing an amendment to the agreement allowing her to pick-up the child from school on the Fridays she has access time.
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What she is, or is not, allowed to do should be spelled out in your custody agreement/order, the entirety of which should be given to the school with instructions that they are to follow the shedule as outlined in the order. You should also put the school on notice as to who is permitted to pick up the child on your days so that the child is not released to the mother. This is the best way to handle the matter. If she continues to go to the school to pick up the child on her non-parenting days, you can file a violation petition. However, you should be careful when you file petitions. Try and work things out before filing. If you file, that might give her an opening to file a modification petition to attempt to modify the parenting arrangments. Speak to an attorney before you do anything.
The agreement is the law of your case unless you and your ex agree to not adhere to it. If you do not agree with her going to the child's school on her whim, give a copy of the agreement/court order to the school and explain that the mother doesn't not have a right to pick the child up without your specific authorization.