CTlawyer, the Free Dictionary defines “sovereignty” as:
1. Supremacy of authority or rule as exercised by a sovereign or sovereign state.
2. Royal rank, authority, or power.
3. Complete independence and self-government.
4. A territory existing as an independent state.
Thus, it would seem that Indian reservations are indeed sovereign (and, in fact, Native Americans were not considered citizens until passage of the 1924 Indian Citizenship Act). States in the US are also sovereign even though in some respects they are subject to Federal law. It would seem to me that military bases and diplomatic compounds are extraterritorial. However, if the child is not subject to US law it would not be a citizen. This includes children of diplomatic personnel so an American military compound or diplomatic mission might be considered US territory for this purpose even though being the child of an American is not generally sufficient (which it might well be).