I suspect that the travels of the Royal Family are at least reviewed by HM’s ministers. As for Abu Dhabi, well, the UK does a boatload of business Gulfside.
Not just reviewed - decided by.
The British Government (most specifically the Foreign Office) decides what countries the Royal Family visits. Technically, a Royal can choose where they go on holidays without government permission as long as they are not carrying out any official visits, but they would never go somewhere the FO actually objected to. And the FO doesn't want them going to Israel. The Foreign Office is pro-Arab and not offending the Arabs is one of their biggest aims in life.