I guess I'm of two minds about whether or not Sarah should have brought Beatrice and Eugenie into Turkey. I don't think Sarah herself did anything wrong, disguise notwithstanding, because she is no longer a member of the royal family. The line gets blurrier when it comes to Beatrice and Eugenie. I honestly don't know to what extent the royals should be involved in politics or politically charged situations. They are supposed to be apolitical, but that hasn't stopped many of the royals--eg. Prince Philip, Prince Charles--from expressing their opinions about controversial topics.
Nevertheless, I don't think that the trip to the Turkish orphanages should be so controversial within Britain. Yes, the British government has to respect other governments, but not at the expense of human rights. The EU was skeptical about admitting Turkey because of issues like the treatment of the children in orphanages, and Sarah's documentary simply helped show that there was a basis for that skepticism.
Turkey was obviously "caught redhanded", and knows it, and is now striking back at Sarah. And yes, in the short-term her documentary might have damaged Turkish-British relations. But sometimes a cooling in the relationship between two countries is inevitable or even necessary. Britain should try to be on good terms with Turkey, but not at the expense of its own principles.
And yet I'm still on the fence about Beatrice and Eugenie's involvement, because their presence could make Turkey feel as though the British government itself (represented by the royal princesses) was directly "spying" on them. I do believe that the royal family should try to stay apolitical as much as possible...but then again, sometimes staying completely apolitical isn't possible even for a royal--or right.