DC is awesome!
With kids those ages, perhaps concentrate on the mall location of Air & Space (Space Stuff - everybody loves Space Stuff!!) and maybe
Museum of Natural History (Hope Diamond, Insect Zoo and Behring Hall of Dead Things) or American History Museum (Old Glory) the first day. They're pretty close to each other.
If you really REALLY like Air & Space stuff the
Udvar-Hazy A&S Center near Dulles Airport is even cooler (IMHO). It's really in VA. Parking is $15, but admission is free.
You'll have a good view of Big Pointy (the Washington Monument) from up top at the Orange Line Metro stop in the middle of the mall. It might still be wrapped in scaffolding for earthquake repairs.
Then the other day it would be fairly easy to do the National Archives (Constitution Magna Carta, etc) in the morning and then Capitol Visitor's Center tour in the afternoon (tickets required) or vice versa.
As for the white house, it's pretty much just looking at it through the fence (and watching tourists flip the bird at it), which you can do any time of day - unless you can get a tour scheduled through your MC's (member of congress') office, which they usually want you to do six months in advance.
Since you have such a limited time, you probably don't want to bother with the National Gallery of Art, Portrait Gallery and things where kids usually get a little bored. The zoo has a couple cool things (Giant Pandas and a Maned Wolf) and the price is right: free.
Geez...now I'm getting homesick.