I am uncertain of how she got a passport for the children without both parent's signature. The law requires both parents to sign for the passport application.
For her to leave the children permanently in the Philippines without your permission is clled parental abduction intenrationally, and for the state of Nevada, interfering with the custody of a child. Even if you are the non-custodial parent, the visitation is considered a level of temporary custody,and the charge is the same. (itnerfereance with the custody or visitaion of)
I believe you have a case to stop her. You can have the child's passport revoked by submitting a complaint to the state department if the child's passport was gotton by forgery.
You can also have an attorney file a petion with the court placing an injunction on travel and the court can temporarily pull the passports.
I can not gaurantee you will have success with any of these actions.
While expressing an intention of flight or denying access to the children is frequently sufficient in many courts to have the physical custody rearranged, it is not universally true.
The court may say that until she has actually committed the act, here intentions would not necessarily be clear.
This is why, if the conditions of obtaining the passports was not followed, and she obtained the passports by forgery, or without your permission, that would be your best approach to limit travel.
ALSO, if the court order for custody included mobility rules, and she does not follow them, then she could be found guilty of contempt of court.
you and your attorney can file to attempt to get:
1. A rearrangement of custody
2. Modification to the order to deny mobility.
3. a temporary injuction and withdrawal of passport for travel outside the U.S.
4. Cause a revocatin of the passport if it was not legally issued. (both parents not having signature or by forgery)
5. Contempt of court if the mother is violating the mobility language of the custody order.