Though you're right about the refusing to except the president's authority.
Not to defend Cain, but I don't recall her usurping the President's authority any more than Adama did, i.e. sticking to the policy that military decisions rest with the military. Cain basically gave no shits about the civilians in the fleet, and wasn't around long enough to stage her own coup against Roslin. I suspect she would
have, eventually, but at least what we got of her didn't show her outright refusing to do what the President told her.