I would imagine you would be unplugging your car in the morning before your commute to work, just as i unplug my phone from its charger when i wake up.
Also living on the east coast (near DC suburbs) and having made a similar road trip to NYC many times, i cant remember the last time i did not spend 1 hour + at a rest stop to eat. refuel, relax, pee, etc.
What car do you drive that does 500+ miles per fill up? My civic will do maybe 450 miles of only highway driving on a 13 gallon tank, and my E350 will do barely 400 on an 18 gallon fill up.