I would take a page from the HBO Movie By Dawn's Early Light which is based on 1983's novel Trinity's Child by William Prochnau.
The President is presumed dead and a successor is sworn in. He with the military advisers, so this can the basics for the military government.
Meanwhile the original President come back from the dead so to speak and tries issuing order but people believe it is a fake. The people who strongly support the president are people who have actually seen him or talk to him.
In both cases you have troops following orders because they come from someone they trust.
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I will not hide. I will not be deterred nor will I be intimidated from my performing my duty, I am a Canadian Soldier.
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