I assume that one way or another you'll probably have a car for the Williamsburg portion of your trip. If so, I suggest you try to include a visit to Jamestown. They built a really nice visitor's center for the 400th anniversary a couple of years ago, then they have the recreated indian village, fort and ships, with reenactors. It would make for a nice morning or afternoon.
If you do not have a car while in DC, I'd probably cut out things that aren't easily accessible by public transportation, like Mount Vernon and Great Falls. Iwo Jima is also not the easiest place to get to without a car, although possible. On the other hand, 5 nights is a fair amount of time in DC and will give you a chance to get beyond the Mall a bit, like exploring Georgetown, the National Cathedral, Dupont Circle.
At your daughter's age, you might consider the Newseum and/or the Spy Museum, although those are not free. The Kennedy Center has free short performances each evening, and a beautiful view from the roof. Consider the art museums including the African and Asian museums under the backyard of the Smithsonian Castle, or the National Portrait Gallery/Museum of American Art, which are co-located in the old Patent Building directly across from the Spy Museum. The Patent Building was the site of inaugural balls in its day (including Lincoln's)--another building which has hosted many of those, and still does, is the National Building Museum.
The Smithsonian museums close fairly early that time of year, so you'll want to plan some evening activities. In October you might catch the NHL Capitals or NBA Wizards at the Verizon Center. Or check out a concert or play or musical at the Kennedy Center, National Theater, Shakespeare Theater or many other venues (even Strathmore, which is in the Maryland suburbs, is easily accessible on Metro's Red Line).
Old Town Alexandria is easily accessible by Metro and a nice place to wander, window-shop and dine.
The Jefferson, FDR, Korean, Vietnam and Lincoln Memorials, and even the WWII Memorial, involve a walk from the nearest Metro station. Consider the on-off buses (Tourmobile and Olde Town Trolley). There are also a couple of bus options that are not particularly well-publicized which can get you places Metro does not go to directly:
http://www.dccirculator.com/DCCirculator.html
http://www.georgetowndc.com/getting-here/shuttle