How much and how long would it take for a parent to file a motion to travel with her sons?

I am a travel agent and I have a client who has read her divorcee decree and the only thing it states is that her and her ex need to give a 2 weeks notice prior to travel out of the state. There is nothing else regarding travel restrictions and vacations. The children at 17 & 14. She contacted her ex various times since the beginning of January asking for consent to take the children on a cruise (17 year old grad present) along with a notarized letter in case she needs it. She does not want to book the cruise until she knows for sure she will not be denied boarding. The 17 year old just went and got his passport himself using his drivers license with his mom. The mother has physical custody of both children. Since the children are older now they do not have much contact with their father so the mom mainly has e-mail contact so she has proof of contact. The father is in arrears in child support and he can not have a passport issued for himself and she believes that is making him bitter to not comply is filling out the requested paperwork. I told her I would see what I can find out while she also does some leg work. I read about filing a "motion to travel" which the court will allow her to take the children on the cruise without the noncustodial parents consent, but how much does that cost, where would she file and how long does it take?