Hello! Yes, the Royal Navy would have a typical chain of command. Since Thorne is not at war, most of Sidwell's tasks would be standard administrative items that would not require his constant oversight. Like most navies, there would be other admirals, but Sidwell receives the most deference due to his close connection with the royal family. Technically speaking, his orders come from the Crown.

As far as most are concerned, Sidwell is on assignment in accordance with what the King and Queen have requested. There may be some rumors of corruption in Castle Thorne's Royal Army and its guards, hence the Queen bringing in another from the outside to root out treason.