I'm currently reading a book on Operation Just Cause (yeah...the most ironic name for an American military move ever), the invasion of Panama in 1989. In it, I found some interesting facts: Billy Carter was evidently a big lobbyist in Washington for the Panamanian government in the late 80s, which helped (sort of) influence American policy towards the various regimes leading up to and including Noriega.
But what is most interesting is that just prior to the invasion, it was decided that the rightfully elected President of Panama would choose a government and cabinet so when the US deposed Noriega a swift move to democracy could be attempted.
Through an odd chain of events it transpired that (just minutes before the invasion began) in a bunker in the Canal Zone, Billy Carter became a Vice President of Panama.
Now...I'm not sure how Presidential succession works in Panama. Truth be told, I'm going to go out on a limb and say the Panamanians aren't so sure, either, or else they'd do it more peacefully.
So your challenge is to have President Jimmy Carter in America, and President Billy Carter in Panama.