Tony Stark's suits are designed to be controlled from inside. Why didn't the President just use it to fight his captors?
How can it be used as a prison to transport him? Was it remote controlled/deactivated?
As Tony demonstrates the ability to remotely control his own suits in the movie, it's not beyond reason to assume that the same would be possible with the Iron Patriot, thus rendering it an effective if rather unconventional prison.
There is a scene in Iron Man 3 when Colonel Rhodes is holding up a bunch of guys in a building somewhere when Tony calls him and asks "Your re-design, your big re-brand, that was AIM, right?" and Colonel Rhodes replies "Yeah". So if AIM did the redesign and updated the software for the suit, then chances are Killian put in a override in the suits software to prevent the wearer from being able to control it.
It is not a mystery anymore. In Iron Man 2, we saw the Russian physicist made such Iron Man suits that can't be operated from the inside. Remember how Agent Rhodes got confined in that suit and could not leave it. The villain in this movie who held the president captive is a scientist himself. As we saw, at the end of Iron Man 2, the suit was retained by the United States government. However, Rhodes took it away. It is presumable no new upgrades have been done to it (at least not shown). So the suit still remains vulnerable and, as @Avner rightly commented, the villain possibly got the equipment to control the suit and connected to it during the upgrade by AIM.