I just bought a Honda PCX 150 just for the reason of taking it with us. I have had bikes since my first Cushman at 8 years old.
My last setup was a TC towing an enclosed trailer with my Harley in it. It was a great set up as I could also carry our two kayaks inside. There was nothing better for getting around and viewing the areas we camped in, but the TC was too small for extended stays.
We now have switched to a 5R and have a front end class III hitch on the front of the truck for the scooter carrier.
As far as the scooter goes I think it is important for the reasons already mentioned that you get something that will be freeway safe. I choose the Honda for it's speed (65mph with two up) and it's light weight (285 lbs loaded).