Tom Clancy explored a similar scenario in his Jack Ryan series (the book Executive Orders, published in 1996), and Irving Wallace looked into it from a racial point of view in The Man (published in 1964).
The Presidential order of succession—beyond the Vice President—has been frequently discussed, and several laws have been adopted, switching around the order over the decades, although none of them have ever had to be put into use. Nevertheless, it is an interesting topic for fiction to explore. And if you’re looking for more on the factual side (what is the designated survivor, how did it come to be, and who has been that person who was one terrorist attack from the Oval Office?), check out chapters 72-77 in my newest book Ranking the Vice Presidents (specifically, chapter 77 is titled “Designated Survivor”).