Nah, it is not.
The Captain is questioning, the legal qualification of Obama to be President. This is not mutiny, nor is it sedition. If the person in question is not legally qualified to hold the office, then all subsequent actions are illegal.
Yeah, it is. If she refuses to obey the orders of her superiors and induces others to refuse as well then it's mutiny. The military does not take kindly to junior officers and enlisted deciding what orders are valid and what are not. Ask Mike New and Ehren Watada how that works out.