Sure he can move the armed forces wherever. However, to use the military in an act of war requires a congressional declaration of war as mandated by the constitution.
Anyway, you're comparing apples and oranges with the Iran hostage situation. Incursions into embassies or on diplomats can be considered an act of war by the offending party. The President could then act to rescue the American victims, etc. Now if the hostiles are associated with a country and that country has declared war, obviously Congress could declare war as well. If it's a group with no national association, Congress can grant letters of marque and reprisal on the hostiles with or without US military involvement. Ross Perot, with Colonel Simons, for example, took care of his EDS men who were held hostage in the very same crisis.
Taiwan and China are completely different. The President is commander-in-chief of the US Military, not World Police Chief.