In all of Star Trek, there are just two dialogue references to a vehicle called "Captain's Yacht", both from ST:Insurrection. I'd rather prefer to dismiss both. After all, Captains don't have yachts. They might have boats or launches or something. But only civilians have yachts ITRW!
The first comes from the scene where Picard fails to hide his little insurrection from his fellow officers.
Troi: "Taking the Captain's yacht out for a spin?"
Now, Troi is actually dribbling with sarcasm here. So it would be pretty easy to read this line as Troi saying "Ah, I see you are equipping our LSL-22 Surface Assault Barge (Heavy) for a mission, Captain"...
The second is more objective, though.
Son'a sidekick Gallatin: "Sir, as the Enterprise left orbit, one of their support craft went down to the surface. It appeared to be the Captain's yacht. Five persons on board."