If your ex has sole custody, do you mean sole legal and physical custody? If the ex truly has sole legal and physical custody then yes, she can take the children out of the country.
If do so causes you problems, then you really need to get moving and take some action to see if you can change the orders to required your permission. To do that, you need some good reason and you need to go to court to get the orders changed.
You should move now, and you should move quickly to retain an experienced family law attorney to review your case. I am available to assist, should you so desire.
David R. Hartwig
801-486-1715
Answered on Mar 02nd, 2016 at 7:30 AM