Dan - I fully support this idea, I LOVE DC.
Family is from the area, so I went a lot as we would travel up to see the great grandparents.
In the past year Ive been twice, and MIGHT be heading that way on Friday...
I, too, recommend staying a bit out and taking a train in.
It'll also save your nerves cause the traffic and parking really does suck.
Finding FREE parking is a PITA, and a lot of the paid spots are 14 bucks...per hour. It's nuts.
I'll echo what was said above about the Air and Space Museum on the mall - it's half closed and you can really look at everything and be out of there in about an hour or less. We did it in 40. Was sort of a bummer, but DO go!
Air and Space and Natural are pretty much in front of each other, with American history a short walk from Natural, maybe two blocks away. Do American History while youre there. See the flag from Battle of Baltimore and other really cool things.
Then, keep in mind, Korea / Vietnam / Lincoln / Reflection Pool/ WW2 are all very close too.
From Lincoln, at night, it's a GREAT view across the Reflection Pool to the Washington Monument (not open right now), with the Capital in the background.
And I dont remember which branch you went, but also just outside of DC is the Marines Museum - it's freaking excellent!
I, with no military experience/history, loved it, and think that due to your background you would too.
And that your kids would like seeing the displays, it's awesome and FREE
Yes, DC aint cheap. Expect to pay a bit more than here for things, Hotels, restaurants etc. But you'll be opened up to so many free attractions it's totally worth it!