The Supreme Court of New Jersey admits that reconsideration motions are rarely granted, but that shouldn't stop you from trying if the judge who heard your matter honestly made a mistake. A motion for reconsideration follows the same procedure as any other motion made in family court, but your burden of proof is greater and you have a limited period of time in which to file.
Take a copy of the court order that you feel is in error to a reputable attorney immediately. You have only 20 days in New Jersey to file a motion for reconsideration. You don't have to retain the lawyer to handle the motion for you, but you need an expert opinion as to whether or not you even have grounds for reconsideration. You can only ask a judge to reconsider her opinion if she overlooked or misread some important information, if she misinterpreted the law, or if you have new evidence that might impact her decision.
Download a notice of motion packet from the New Jersey Courts website. Use the one labeled "Family Multipurpose Post-Judgment Motions." Do not use the appeal forms. They apply to the appellate court and your motion for reconsideration must go back to the same judge in superior court who issued the order you are asking her to reconsider.
Complete Form A, the notice of motion. Copy all the information from the caption of your order, including the docket number, onto the beginning of this form. Enter the date of the first Friday after 24 days have elapsed as the date you want the judge to hear your motion. Check the box marked "other" for the relief you are seeking and write in that you would like the judge to reconsider his ruling. Print out Form E, the notice to litigants, and attach it to your motion.
Write a certification to support your motion, Form B on the state's website. Explain why you feel the judge erred. In all likelihood, he is not going to appreciate you telling him that he made a mistake, so present your facts in a calm, rational, non-accusatory manner. State the facts that he overlooked, the point of law you think he misinterpreted, or the evidence that was not available at the time he issued his order. Attach as exhibits any documents you have that support your position. Your certification can't be more than 15 pages long.
File your motion with the court and serve it on your adversary on the same day. If you hand-deliver it to your adversary yourself, have her acknowledge receipt in writing. You can also hire a private process server. It's important that your adversary receives it on the same day you file it, so it's not advisable to use the county sheriff or postal system for service. You should also hand-deliver your motion to the courthouse yourself for filing rather than rely on the postal service, because the timing of a motion for reconsideration in critical.