Please note that I am not licensed to practice law in NY. However, unless there's something unique about NY law, I don't believe that you need to file a motion for criminal contempt. In Mississippi, for example, if a party is in contempt of a divorce decree or child support order, etc., the other party files a motion to hold the party in civil contempt or a motion for a "show cause" order in which the other party is asking the court to issue an order demanding that the offending party show cause why he/she shouldn't be subjected to some sort of sanction.
If the offending behavior is egregious enough or the latest in a series of conduct that runs afoul of the court's orders, then the court has the power to order the offending party to jail time. But this is usually reserved for the more flagrant violations.
You do not need a lawyer to file this motion, but to ensure you're in compliance with NY procedure, it wouldn't hurt to at least consult a NY attorney before you file anything. I hope this helps.
If you are looking to file your own motion, you can go to the court clerk where your matrimonial action is filed (I assume Supreme Suffolk, Riverhead) and ask how you can go about doing this. The clerks are particularly helpful to pro se litigants.
I'd have to recommend an attorney for this particular issue. Although matrimonial courts are accomodating to pro se litigants, the procedures involved with a contempt motion are stringent enough for a lay person to fail in bringing it. For example, the Judiciary Law requires that the language on the notice for a contempt order contain a specific warning and that the font of the warning be bold and 8 point . If there is a friendly clerk available to assist you in the matrimonial part, then you might be able to do it yourself, but I think it's best to have an attorney handle the many details involved in bringing this kind of motion.
It's also correct that you would not be moving for criminal contempt; your rememdy is one of civil contempt (designed to vindicate a private right), which has a lot of bite. Imprisonment is a penalty for disobedience of a court order under the civil contempt statutes, but this is rarely imposed.
Sign up to receive a 10-part series of useful information and legal advice about the divorce process.