This - like most things comes down to the kids and their interests. DC is like any other city - filled with families that do fun things. So you can go to DC at any time - weather or not your kids are into it is something completely different.
My suggestion is ALWAYS do things that are empirically fun to do for your family. Do the museums etc but then also do LASER TAG or BOWLING or MINI GOLF. Go to Chucky Cheese (if your kids are into it). Don’t turn it into a week of MUSEUMS 24 x 7. Look kids - MORE history.
So whatever it is you do / and when you plan on going - do things that you as a family would consider fun.
There is also the National Zoo (which I didn’t particularly care for but it is free and what kid doesn’t like a zoo).
Fold in FUN things.
We travel a lot with the kids and do a lot of “seeing” of things - but we also ensure we do things that the kids are sure to like and that are FUN.
Also - as previously noted the mall is LONG - LONG - LONG. We went from the Capital down to Lincoln and back in June (we aren’t the smartest people obviously).