After all, President Ellis was still alive, and the Vice President was only the Vice President. If their connection to the Mandarin were exposed, they would inevitably face a joint crackdown by the government and military. Even if the Vice President wanted to help them, he would be powerless by then!
Moreover, Pakistan was nominally the Mandarin's stronghold. If Tony Stark went there, it would mean he had taken the bait. Facing a group of terrorists, Tony Stark would not be overly guarded. On top of that, he did not know how Extremis could counter the Iron Man suit, so he could easily be captured if he let his guard down.
But if Tony Stark did not go to Pakistan and came to the estate instead, it would mean he had seen through their scheme. He might even know about their connection to the Mandarin. He would certainly be much more cautious and vigilant then, making Tony Stark far more difficult to capture. And if Tony Stark escaped after the battle, they would likewise be completely exposed.
Since that was the case, they might as well withdraw outright and leave behind an empty estate. On the surface, this estate had no connection whatsoever to him or AIM. They had always been very careful to remain hidden, and as long as they were not caught in the act, no one could link them to the Mandarin!
The feasibility medical report and related materials in Chad Davis's possession alone were not enough to prove their connection to the Mandarin. But to be safe, Aldrich Killian decided to hide himself deeply until the final mission was completed. Unless it was the final moment, he would not show himself easily!
As for the Iron Man suit, he naturally had a more reliable way of