FWIW, DC is crazy but the last time we went, we stayed well outside of DC and took the train in. No driving involved, get dropped off close to whatever we wanted to see.
I bring this up as DC has a number of free museums which might be worth seeing. I enjoyed seeing the free stuff, and that can free up money to see other things.
There's an air and space museum that I recall being easy to get to and from on the outskirts. We hit that up on our first day, then went to the campground we were staying at, and the rest of our trip we'd just drive the 15 minutes or so to the outermost hub, park, ride the train in. Very low key and easy. Maybe hit up stuff outside the city on the way in/out, or if it's a week long stay, you could alternate days in and out of the city.
We do the same thing when we go down to NYC, park at Southeast Train Station and ride down. None of the traffic (well plenty in CT). I always get a kick out of passing through Valhalla.