I would agree that the first person who should be filing the contempt motion would be your mother, as she was a formal party to the divorce case along with the agreement. However, if there is a valid reason why your mother cannot or will not file, I believe you can self-petition. And while children self-petitioning on child support matters is quire rare, I disagree with the other poster's implication that it is impossible. In any event, I encourage you to call a Westchester/Putnum Child Support lawyer to schedule a consultation.
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I am forced to bear bad news. You were not a party to the divorce, so you have no standing to enforce the decree. Contempt is not a legal action that stands on its own; it is an extraordinary remedy for violation of a order entered in a court action. Only the parties to that action have the legal standing to enforce orders entered in that case.
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As the other lawyer said, you can't enforce the divorce agreement. You can, however, see if your mother will move to enforce the divorce agreement. She can file a post-judgment motion to enforce his agreement in the county where she is. She will need proof of his lack of payment.