I'm not suggesting it needs to be an RV cabinet. I'm saying if the OP wants the style and finish of the cabinet to match what is used throughout their TT, they'll want to get something for their specific brand from the dealer. Finish colors and profiles used on RV cabinetry and trim varies a lot between different brands.
If it appears that something better is needed to hang the cabinet, if you look at the floor plan, the cabinet would go over the toilet that is on a 45 degree angled wall. The cabinet would be only inches away from a corner stud on each side. (It appears the that cabinet over the sink would not be as wide as the angled wall behind the toilet.)
What I would do is cut out a square of the luan plywood with a sharp utility knife slightly smaller than the dimension of the cabinet. Then slip a piece of 1x2 horizontally inside the wall and secure it to the stud on each side with angle brackets and screws. The wall could be thicker behind the toilet if the waste vent pipe runs up inside it, which could be 2 1/2" deep with a 1 1/2" pipe which will still allow 1x2 to be slipped into the wall cavity.
No special or expensive tools required.
Without seeing it, you *might* also be able to slip in 1x2 (or 1x3) vertically inside the wall (again, with cutting out a section) and glue it in place to the inside of the wall on both sides. That way, the cabinet weight would be supported from the interior and opposite sections of wall paneling which should be more than adequate for the low weight of a medicine cabinet.
If you want any cabinet parts or a cabinet, you'll need to order through a dealer. They will have access to all this stuff in case repairs or replacement is needed in a customer's RV. Just watch how they propose to have it delivered to them. I ordered an 8' length of molding once and they soaked me $60 for couriering it. I should have asked first... They should be able to have it come in along with regular shipments.
Just another thought. Does the vanity cabinet have a blank panel on the lower part of it? That's quite common. If so, you might be able to get a door (from the dealer) from a Lacrosse model that will be of suitable size to fit over the opening. That's what I'm going to do with our new TT.
It's interesting looking at the floor plan for that model. Considering how long the TT is, there's little space inside the bathroom for storing towels and other bathroom stuff. Obviously designed by a man. :B