Your wife and son will enjoy the Smithsonian on the Mall here in DC. She can easily take in the Freer and African art museums by Metro from Alexandria and then lunch at either the American Indian Museum or, my favorite, in the old National Gallery of Art building that has a sit-down café of good atmosphere. Then the afternoon at the National Gallery where the Da Vinci masterpiece Ginevra is on display and then next door in the IM Pei National Gallery building for whatever is on modern there. Across the street (Constitution Ave. NW) are the National Archives.
A great place to go is the Philips, which is closer to Dupont Circle, also Metro accessible. Google to see what's on there in the way of special exhibitions.
Not sure what interests her in shopping, but the Tiny Jewel Box at Connecticut Ave. & M St. NW is very good, and, if she wants to outfit you, it's just across the street from Brooks Bros. clothing. For a smaller and less expensive place, go into Compton's on G St. NW just half a block west of the Old Executive Office Building and ask Susan for either sale items or estate jewelry.
I'd still have gone to Prince George's County from Alexandria as it's a pretty straight shot up the eastern side of DC: 14th St. bridge; southeast expressway leading to Baltimore-Washington Parkway; then off at the Greenbelt exit and a few miles east to the turn north that will eventually get you there...
Regards, Tim
