Well worth the effort to visit, but sounds rather high. I have visited D.C. on vacation 3 times, enjoyed it all.
Last summer we did the same thing, except went by bus, for less than 700 bucks a head.  Went with sister's church group from S. Carolina by bus, 4 nights in a Hilton, all meals ( nice places ) ,guided tours of Arlington Cemetery, White House, Capital, Smithsonian, Mount Vernon, Senate Building, and a few more places. Very well worth the small price, but you are correct, no time to really absorb the history in 4 days. As this may be your only visit to the swamp, stay as long as possible, visiting as much as you can. Take plenty of pictures.
I agree, do not use a rental car. Too much hassle parking, getting lost, etc. Very time consuming.
A place that surprised us was the Bible Museum, extremely informative.
I took my kids when they were pre-teen, they enjoyed it,but did not really grasp the real meaning of our history.
No problems in the big city, folks were nice to us country people.