Passport denial is not that easy. You must be on a list developed by the state; it's true she may have reported the arrears, but she cannot be the authority to deny you your passport. This is in place so the authorities have more assurances you won't cross borders and ignore your legal responsibilities here. The best thing to do and probably the only action you can take at this point is to pay up the arrears or significantly pay them and contact the prosecutor's office and see if it can get your name off of the passport denial list. You need to show compliance but that does not mean your name is automatically taken off. It simply means you get the chance to petition to be eligible for a passport.