Where exactly was Trystane Martell, the Dornish prince (son of the Prince of Dorne, Doran Martell) in the Season 6 opener, "Red Woman"? Where was his boat at the time? Was it in the city of Sunspear, capital of Dorne, or Blackwater Bay, near or in the harbor of King's Landing?
The events in Dorne happen in Sunspear, the Dornish Capital. After the Dorne Prince Doran is murdered, the camera shows the outside of the ship Jamie, Bronn, Myrcella, and Trystane used to leave Dorne (right before the camera cuts to the inside) where Trystane is painting eyes on some stones. The ship is clearly in outside of King's Landing harbor, as has been shown many times in the series.
The camera cut can be seen at 2m10s in this youtube clip (embedding disabled).
King's Landing Harbor as seen in s02e06 "The Old Gods and the New", when Myrcella was first sent away to Dorne.
The only logical explanation is that he was indeed in King's Landing when murdered.
Also note the difference in the Crownland Ships and rowboats compared to the Dornish Ships and rowboats.
Have we caught Prince Trystane's killers? I expect it was Mother.
There is no way they could try to catch the killers if everything happened in Dorne, not mentioning that they probably wouldn't even know about the murder.