If you have sole custody and the child has a different last name all is good, as long as they have a passport. Have done it several times with my daughter. Take the divorce decree and of course the passport. If joint custody, then yes other parent has to concent to the child leaving the country. you can have it notarized at the airport. The DD also has to be an official copy you get from the courts, not just a copy. But they require that when getting the passport for the child. They will order it from the courts before they issue the request for the passport.