Here are my suggestions.
1. Rent an rv for the trip. It is likely your Audi is not towable 4 down. If you rent something 25' or less you don't need a tow car.
2. Tow pop up behind Audi. Stay in hotels when needed.
3. Drive Audi to old classic hotels built in most national parks early in last century. Such as El Tovar at Grand Canyon. Awhanee yosemite. Paradise inn mt rainier. Many glacier at Glacier. Bring tent in back of Audi. Stay in campgrounds some of the nights and classic lodges other nights.
Watch Robin Williams RV movie.
