If the order is 60 days then you need to give him 60 days unless you get an order of the court. The notice is to allow the other party to object to it.
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While it is true that the 60 days notice is to give him an opportunity to file a motion to modify custody, that isn't the end of the story. First, your order that you cannot move more than 60 miles away is unique and seems to indicate greater restriction by the court. Second, you still have an existing court order. You will be violating it if you do not give dad 2 days/week. So I would file a motion to modify the parenting plan. You have a pretty good reason to move. You will have most of the school year, but dad will get extended time during breaks. Talk to a lawyer in your area, because this is a complex area of law. There are a lot of variables that you don't mention.
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