Your kids are the same ages as mine so being inside the district will be a huge benefit. I would look at the Hilton Garden Inn on 14th St. NW. It is located perfectly for walking to the monuments, but it has reasonably priced suites with a sleeper sofa that also easily accommodates a roll away. That way, each kid has their own bed and you have your own room. It's tight but will deliver a good nights sleep for all in an unbeatable location. Plus, the restaurant in the hotel is first rate and reasonable.
There are some must sees and do's:
1. Ford Theater
2. Lincoln Memorial at night
3. Reserve your ride (now) to top of Washington Monument if open.
4. Bureau of Printing and Engraving (kids will love seeing all the money)
5. Smithsonian, of course.
6. Senate and House tour. Hopefully they are in session. We were able to watch from the gallery as Charlie Rangel voted, by mistake, with republicans on a bill. Other dems came rushing to his seat just before vote closed to have him change it. Pretty funny.
7. Duck Tour - This is still our favorite. You ride around town in a World War II DUKW amphibious boat/truck hybrid seeing the sites, and then it plunges into the Potomac river and you get to see DC by water. They'll even let the kids drive the boat. Best $40 you'll spend in DC.
Hope that helps. Good luck!
Don’t forget the National Archives to see the Declaration and Constitution up close ... really breathtaking.