We stayed at the Capitol KOA in Millersville, MD which is about 20 miles from the heart of D.C. They have a shuttle bus for a fee, but the parking in the city is very expensive, making the shuttle economical at times. We weren't intimidated driving in the city, but we had our truck, not towing our rig or in a MH.
We spent five days there, and would have liked a few more. I would stay in the area at least 7 days and map out an itinerary before you go so you can hit as many attractions as you can in the same vicinity.
You can go through your state senator's office and get free tours of the national mall and other attractions (visit your senator's online websites). Be sure not to miss the Steven Udvar-Hazy National Air & Space Museum at Dulles Airport. It's different than the Air & Space Museum on the mall, and much better. We thoroughly enjoyed Arlington National Cemetry, Ford's Theater and the guided tour of the Capitol. We took a drive up to Gettysburg and sadly only gave ourselves about 3 hours to visit, but it's at least a whole days experience.
Enjoy your trip!