At the end of the episode, Jamie and Claire break the music code and find out the Duke of Sandringham secured $40,000 for Prince Charles from the English nobles. They then exclaim that, since he's already had dealings with Dougal, that he is "playing both sides" and "hedging his bets." I don't understand why they say this. Aren't Prince Charles and Dougal on the same side, i.e., they are both Jacobites and want to have the Stuart line returned to the throne?
He's playing both sides because he is English aristocracy who is in theory supportive of the king. Since he's secretly raising funds for the Jacobites, that makes him supportive of the Prince. He's trying to keep his dealings with the Jacobites hush hush so if they lose, he can claim innocence, and still be in the good graces of King George, but if they win, he can say, "Look at all this money I raised for you," and be in the good graces of the Stewarts. Make more sense?