I have a clone of the MasterTow, a Stiehl Tow Dolly.
I put a 3 inch caster wheel right behind the coupler, so I don't have to lift the tongue to move it around.
Once the car is off, if roomy, I back the dolly in like a short trailer. If its tight quarters, I un-hitch it and we each push a fender to steer it into the site. Then I back the RV over the tongue to shorten things up.
A longer pull thru sites, I just leave it all connected.
If your handy, throw the dolly to car safety chains away and pick up 2 vinyl coated safety cables. They can be thread thru the cars front wheels and connected to part of the dolly frame. Much better then laying down under the car.