On the issue of travel outside the US, the gatekeepers on this question are the US State Department, and the airline. The usual requirement now since a passport is necessary to travel out of the country, is that both parents must consent to the travel. Court orders now have provisions that deal with this eventuality. You should check with the US State Department (for the passport), and the airline for their particular needs. Do it now, and do not wait until a few weeks before a trip. Passports can take as long as 6-8 weeks to obtain, and that is if all signatures are readily available. In a difficult case, the court may order a parent to sign the necessary consent for the child to travel. This would be in the context of a Motion to Modify, which would be filed in the county that has continuing jurisdiction over the child.