Look, I'll make this simple so that even an idiot such as yourself can understand the issue. The UCMJ does not exist separate from the Constitution, but operates with in the Constitution for the purpose of giving the Government direct control over all military personnel so that the Government can undertake the all important responsibility of National Defense.
Look at it this way : Both diplomats and military are government employees. Both the military and the Diplomatic corps are specifically required to take official oaths of allegiance to our Government as a prerequisite for official service. Both groups are required to perform necessary government functions within foreign countries. And it is necessary for our government to maintain direct jurisdiction and control over both groups so they are able to carry out those functions. Think of it as two arms that are part of the same body.
The UCMJ allows the Government to exercise full authority and control over military personnel regardless of the area and laws in which they happen to reside. It doesn't matter what the laws are in a given state or municipality. Even if a soldier commits a "non military" crime outside of a military installation against a civilian, the soldier is still tried by military officers in a military court. The government maintains control over the soldier regardless of the jurisdiction of the state or local in which the crime occurred.
Likewise, even if a soldier or officer commits a "non military" crime such as rape or theft against a foreign civilian in their host country (outside of a military installation), that individual is still tried by our military officers in a U.S. military court because our government maintains that it's jurisdiction (via the UCMJ) still supersedes the host nation's own jurisdiction; even in circumstances such as these.
Now, there may separate treaties or official agreements with a particular country that does allow them to prosecute our military personnel in their own courts for a particular set of crimes. But this kind of arrangement is contingent upon a particular contract of treaty with the nation in question. Our government wants to maintain control over all military personnel as SOP.
Olson and Tribe contend that this kind of *supra -national* jurisdiction and control works both ways for citizens involved with military service that have taken an official oath declaring direct and immediate allegiance to our country and its government. Their children are citizens by birth, because the parent is subject to the full and complete jurisdiction of the U.S. Government. Jurisdiction, as Trumbull specifically stated, is defined by national allegiance. The parents' status at the time of birth defines the child's status at birth. It works this way with all groups.
And remember, the family was outside of the country at the time because because of the parent(s) military duties.
Congressional Code of Military Criminal Law applicable to all military members worldwide.