Two kids under 8? I'd go absolute miminal irrops risk and minimal hassle on this one: morning flight, nonstop LAX-IAD.

If all goes well and you roll into Dulles in the afternoon, maybe visit that Smithsonian air museum out in Herndon. Grab dinner in Reston, have a stroll around, head back to Dulles at 9 or so. There really isn't enough time to go into DC itself.

No connecting itin is going to give you any time to visit another city.

If you want to add a day to the trip, then you have a bunch of options...although you may end up with cranky kids if you're doing back-to-back redeyes and trying to do a ton of sightseeing in between.

To preserve the joy/sanity of the international trip, I'd keep the transcon part of the trek as simple as possible.