I'd give you a tour myself if I was still working down there, alas...
I'd recommend looking at the air and space, both the downtown building and, if the kids are into aviation the building out in dulles. I'd also stop by the national history, and take a look at the archives. If the kids like art, you may also want to stop by the national gallery, there is a lot of really cool stuff in there.
The kids will love the National Postal museum, and although I've never been, the Spy museum gets good reviews, if it is known to be a little expensive. In a similar vein, the newseum is also pretty neat. The monuments are pretty cool, I guess, but I've seen 'em a thousand times, and frankly I find them a bit boring, I'd only budget one day to spend walking around the memorials. I think that you will find the ZOO to be a much more enjoyable way to spend your outdoors time in DC.
Metro is really easy to use and you shouldn't have any problems with it, although it is really expensive, and cannot be used to get you out to IAD. Still it beats driving and parking, and it certinaly is a whole lot cleaner than the new york subway. I think that the metro still sells day passes for 7 dollars which may be a better value than simply paying for each ride.
One bit of advice, however, stay off the metro at or around rush hour. The crowds will not be too friendly to people who don't know their way around the system at those times, although Washingtonians are usually quite friendly in other circumstances.
You should also include a visit to some of the less visited parts of DC, including Old Town Alexandria (metro runs out there) and Georgetown (metro doesn't run there although the circulator bus does.) I'd also take a look at some of the old buildings along Mass. Ave and near Dupont circle, and perhaps looking at Adams Morgan if you are adventurous.
If you have time and really like planes, than a trip to the Gravelly point park is in order, it's hard to beat 737's 10 feet over your head!
You have picked a good time to visit, DC isn't too terribly hot in the spring and if you are lucky, the cherry blossoms will be in bloom around the tidal basin.