Since the international headquarters of the organization I work for is in DC, I am usually there at their expense these days, but prior to my going to work for them, if I had to go to DC, I like to stay in Fredericksburg in a motel and take the VRE train into DC. Parking is free, unlike at the metro, and you save all of that maddening rush hour traffic.
I have also traded into the resort mentioned, using it as a base when I was there for a presidential inauguration. If your kids like the history of the War Between the States, the resort actually sits on part of the Chancellorsville battlefield and a couple of other battlefields, Fredericksburg and one from Grant's 1864 campaign (Wilderness, I think) are very close.