That sounds like an awesome summer vacation!
Unfortunately, you cannot flat tow a Toyota Tundra 4x4. Toyota states this in the user manual for the Tundra.
Flat towing a vehicle that isn’t properly equipped can wreak havoc on your car’s transmission. Basically, if your car doesn’t have the right type of mechanisms that will keep your transmission lubricated when the wheels are moving and the engine is off, it cannot be safely towed with all four wheels on the ground—sometimes called “four down.” Your best bet is to get a towing trailer so that the wheels of your car won’t be moving at all.