This is called DEMOCRACY and REPUBLICANISM (acting for the sake of the people one's in duty for).
In fact apart from being a vassal country (of another or any kind of international organization) why a country would let its soldiers be judged by other countries. And I don't see why any elected president and administration would let that happen.
Many supranational laws and agreements are taking over countries' own constitutions. This is often one request of the agreement. Those countries are mainly democracies. The international laws are administered, interpreted and ruled by unelected burocrats. Those are so powerfull that the main goal of a mediocre politican is to please them to become one day part of their team (or any other gratitude), whatever the interests of the people who elected him are.
This is becoming so true that in many democracies burocrats are interpretting their job as being a grade of a system topped by their higher grade being an electoral mandate and so, those elected would have to be part of the system. This is democracy changed into an ideal Soviet Union system.
Then those elected burocrats, which would be those chosen among the most competent, system wise, would make their most insane ideals become true, an administration in charge to control those elected against any unacceptable decision of the voters (if this could ever happen in such a system).
Now this is what happens when civil servants are authorized and even encouraged (who else would better know how everything works ?) to be elected at the top of its administration. By no means should them be allowed to be candidate in their own administration. This is like filtering the old and crippled, the too young or anybody based on some mischief or lie that compromises his free action when in duty.
Because of their narrow minded objective at work, the burocrats only purpose when in charge is to transfer the management of true and fictituous problems to new and made on purpose administrations. They see the best in those in charge to check the other.
So people should make so to keep their country out of the control of any international administration or so called treaty (as this is checked by a supranational administration too). Any different behaviour of yours would mean that you do not believe in democracy. It is interesting to note that when a party usually opposing wins elections the country signs such treaties so that the party may hold a postion by another mean than election. As for how to handle such a threat, in Denmark such a commitment should be accepted by two successive elected assemblies as for constitutional laws.

__________________
From SR