You are not suppossed to submit legal argument aftet the oral argument. If you lose the motion you can make a motion to reargue based on the judge's misinterperation of the law.
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You will also have the option to appeal the ruling (at some point).
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I suspect that you do not have an attorney, so your confidence that the judge doesn't know the law and you do may be overly optimistic. If you believe that the ruling is against you and based upon that error alone or as the significant reason for the adverse ruling, without which s/he would have ruled otherwise, then you may timely file a notice of appeal after the ruling, and the perfect the appeal. You need an attorney, and one reason is you didn't have one now or earlier. Good fortune.
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To better understand how to answer your question, you may need to provide insight as to what kind of case you have (as you checked off that the case is involves "child custody," yet is simultaneously in "Family Court" & "Federal Court"). That said, you cannot generally submit anything to a Judge after a motion has been marked as "fully submitted" for decision. If the decision comes down against you, you'd need to determine whether to file a motion to reargue, a notice of appeal, or both. In any event, I highly advise that you schedule a consultation with a NYC Family Law attorney.
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