Having just spent a few days in Salzburg, I would echo what the others are saying. While the drive to Berchtesgaden is fairly quick (we had a car as well) I think trying to cram all of that into one day could be a bit much. If you have more than a single day in Salzburg, I would devote one day to the old town area and another to Berchtesgaden, etc. Salzburg is a very walkable city, so if you decide to go this route, plan on parking your car and take advantage of the very handy bus system there (they sell 24 hour travel cards on the buses for less than 6 euro each).
Best of luck!