Hi Jonathan - Henry was definitely the heir but my understanding is that Charles left Scotland in 1604 and was in London in November 1605 and may well have also attended the Parliament, so the King and his two sons could have been dead. The plot to kidnap Princess Elizabeth, as next in line to the throne, is an interesting one and included in Remember, Remember the 6th of November.
I agree a civil war may well have happened but it would have been critical who took control immediately after the event. I've put what I think is an interesting take in the novel on this point, with a lot of of focus on the role of Robert Cecil, the Earl of Salisbury and Spymaster General - but I don't want to give away too many spoilers.
It was a very fascinating time - England concerned about Europe, terrorism and government surveillance.