Dolly is easy to store, just back over it so the rear overhang covers about 80% of it.
Admittedly I could have backed up a little more in this pic.
As for getting stuck somewhere that we had to back up at..hasn't happened (granted with our 25ft Axis we can easily navigate a cul-de-sac pulling the car--in fact we often do since our house is off of one! LOL
The green in the foreground is part of the circle of the cul-de-sac).