I live in the Chicago area. Well versed in heat and humidity that’ll rip the gizzards out of ya! Lake Michigan is one big-ass humidifier!
LOLOLOL. Believe me, I have lived in Chicago and I assure you that Chicago has got nothing on DC in terms of heat and humidity. Nothing. Not a thing.
Lucky for you, we're having a cool summer so far and the weekend of the Fourth should be bizarrely nice. You should have no trouble at all.
I’ve lived in both Chicago and DC .. trust me, by comparison Chicago is one big breeze. You are lucking out in that the present forecast is mild for a DC 4th. They are forecasting daytime t-storms, not evening (so far). Crowds assemble on the Mall from very early in the day. If there are storms, the Mall gets cleared until it passes.
The park service has a ‘plan your trip’ feature. There’s a downloadable map. http://www.nps.gov/nama/planyourvisit/maps.htm
There’s also a folklife festival on the Mall that precedes the 4th, so that would be fun for your family to see. http://www.festival.si.edu/visitor/general.aspx
You will want to see the WWII memorial (kinda hard to miss).
Plan to do everything on foot. You can plot it all out on that map. The Mall is geared to tourists on foot.
Bring broad brimmed hats, sunblock, neck/shoulder coolers, and plan to buy lots of expensive water (save the bottle to refill at fountains if you want).