Even if you trust your spouse to have the best interest of your child at heart, is important to realize that your ideas and those of your counterpart might be different. in fact, it would probably not surprise you to learn that disagreements on child rearing are one of the most frequently cited reasons for divorce in Texas.
Unfortunately, if you were a service member married to a foreign national, or if your ex-spouse were stationed overseas near extended family, this disagreement could potentially turn into a complicated legal issue. This is especially true if the country in question was not a party to the Hague convention.
The Hague Conference on Private International Law website describes the treaty as a multilateral effort to protect children from abduction across international borders. In short, it could provide a framework for you to ask the government to intervene on your behalf if someone kidnaps your children and takes them to another treaty country.
Some countries view this treaty as an unnecessary yielding of local power to international authorities and do not participate. Others may be a party to the treaty, but their judges' ideas about child custody may be different than your local court's presumptions. Even under the most favorable circumstances, it could be difficult for you to help your child return back home to the United States.
The situation is complicated, but there are some things you might be able to do in order to prevent these issues from happening. Divorces involving military personnel are already complicated, but it is probably still worth your time to consider future risks of an international nature and address them.
In this situation and many others, it is usually best to consider the details of each case individually before taking any action. Therefore, please do not view this as advice. It is only meant as background information.