Is American law subject to and subservient to foreign law?
In regards to citizenship, its allegiance, and obligations, I'll defer to the U.S. State Dept's information on that:
"Each country has its own citizenship laws based on its own policy. Persons may have dual nationality by automatic operation of different laws rather than by choice.US State Department Services Dual NationalityThe U.S. Government recognizes that dual nationality exists but does not encourage it as a matter of policy because of the problems it may cause. Claims of other countries on dual national U.S. citizens may conflict with U.S. law, and dual nationality may limit U.S. Government efforts to assist citizens abroad.
...dual nationals owe allegiance to both the United States and the foreign country. They are required to obey the laws of both countries. Either country has the right to enforce its laws, particularly if the person later travels there."