I just asked an attorney friend and he said: Generally a child may not be taken out of the jurisdiction without: (1) consent of the other parent or (2) permission granted by the court. And he said, courts generally are not going to turn down a parent's plan to take a child on a reasonable vacation, unless there are indications of foul play, i.e. she's planning on moving to SA, etc.
This friend is helping someone who's wife took their son while in her custody (they share custody) and moved to another state. He can't simply request she return him, she already has filed for sole custody in the new state, so he has to file for a court order for her to return the son here and serve her in the new state, he can't charge her with parental kidnapping for some reason, it's a mess and a legal nightmare, not easy at all.
I know a lot about this topic because my son was kidnapped by his father and taken to Nigeria for 10 years, 11 months. Even though parental kidnapping charges were filed against his father here in CA his government didn't cooperate or even acknowledge he'd done anything wrong, and I couldn't simply have picked him up if I'd known where he was. I and my son are one of the reasons the law was changed and both parents now have to sign for a child to obtain a passport.
That being said, this is what the State Dept says about International Child Custody Disputes:
There are legal limits to the assistance that U.S. authorities can provide to parents involved in a child custody dispute. When an American child is abducted overseas by a parent, the U.S. Government's role is to help the remaining parent by locating the child, monitoring the child's welfare, and providing information about child custody laws and procedures in the country where the child has been taken. Consular officers overseas can issue a U.S. passport to a child involved in a custody dispute, if the child appears in person at a U.S. Embassy or Consulate, and if there is no court order from the foreign court of that country barring the child's departure from the country.
Parents who are involved in a custody dispute overseas should find out whether the foreign country to which the child has been taken is party to the Hague Convention on the Civil Aspects of International Child Abduction. Under the Hague Convention, a child who has been wrongfully removed from a parent may be returned to his or her place of habitual residence.
Yet, this is all for actual parental kidnappings, not vacations. So basically you need to do whatever you need to do before she takes him out of the country because otherwise she'll have him the time she intends. Find out if you legally CAN file kidnapping charges against her if she takes him on "your" weekend, if she informs you beforehand maybe you can't. Find out if she has to petition the Court for permission if you deny it, or if she even technically needs it. Seek out an attorney tomorrow, because unless someone who answers you here IS one we don't know what the law entails, and trust me, it can get truly complicated, and it doesn't always make us happy.