Roberts was not going to refuse the swearing in without deadbang reason not to. Maybe Robert E'ffed up the first time in swearing in Obama on purpose? It is not a realistic scenario for Roberts not to do so, and because he went forward with it, doesn't support your faulty premise that Obama is qualified to hold office per Article 2, Section 1, Clause 5 of the Constitution.
There is nothing unlawful about a deployment order. Obey it, or be punished.
Deployment order come from the SECDEF a cabinet position that performs delegated duties from the President of the United States. The President derives his authority and legitimacy from the US Constitution. If he is in violation of said Constitution because he is not eligible to hold office, he would haves no legitimacy or authority to give orders, therefore, the orders he gives would be unlawful.
Has anyone in Congress - which has the power to remove a President - or the Supreme Court shown any doubts? Has any case gone forward?
No, and no. Therefor, the military needs to assume he is legitimate unless and until someone demonstrates a reason he is not.
An officer refusing to obey GWB in 2001 would have been full of crap. So is this one.