Hi,
Your Tundra will limit your ability to tow something large enough to haul the VW. Most toy haulers only have a 1,000 pound rated ramp, and most will also be limited to about 2,000 pounds total cargo rating in a travel trailer configuration. Larger fifth wheels will have a 3,000 - 5,000 pound cargo rating, but also come with a 3,000 - 5,000 pound hitch weight, that your Tundra will not handle well.
My suggestion is to find a lightweight travel trailer that your Tundra can tow, and then drive the car separately. Look at the Lance lineup, and other light weight travel trailer lines. Your truck should be able to handle about 800 - 900 pounds of hitch weight, not much more and still handle well.
When moving, I would suggest that anything heavy be put into the car, not the truck. This will increase the overall load being carried by the car, and get the truck/trailer GCVWR as low as possible.
If you had a dually F-350, then I would suggest several of the 38 -43' long toyhaulers, and then figure out a way to load the car without exceeding the ramp weight limit. But you don't have a dually with a 5,500 pound cargo rating. Those toyhaulers will have a 15,000 to 21,000 GVWR, that will exceed the GCVWR of your Tundra. The tundra tow rating is probably less than 10,000 pounds.
Good Luck,
Fred.