So as far as the actual show goes, my guess is that Doran has no idea what's going on in King's Landing with the Sparrows, or he wouldn't allow either Myrcella or Jaime to return there. The Martells and the Tyrells will have to work together to dismantle the Sparrows, because neither family can allow Myrcella and Tommen to be outed as the products of incest, or both families lose their connection to the throne. This is where we'll really have to wonder if the High Sparrow is a true fanatic, or if he's smart enough to make concessions for the good of the realm. If he outs Myrcella and Tommen, the rightful king becomes Stannis Baratheon, but Stannis is a heretic. I honestly think the only person with an actual claim the Faith would support would be Daenerys, but god knows when she'll ever make it across the Narrow Sea.