C.O.
If you plan on visiting the White House you need to contact your representative to get tickets. You might not have enough time to get tickets - they say 4 to 6 weeks notice.
I would take the Metro ANY chance I got. If you used to live here you know that DC in July is WICKED humid and HOT and parking SUCKS. Buy the smart trip cards in advance so that you don't have to worry about standing in line with kids in the Metro to buy or reload cards.
With kids that young? I would DO ONE THING - Zoo or museum. Parking for the Zoo is a ZOO - so I would take the metro (Red line and get off at Woodley Park/Zoo) and walk up from there.
With kids that age? I wouldn't plan on spending much time in any museum as they will most likely get bored. Especially the 4 and 18 month old. I don't know your kids so I don't know how they would handle things like this either. I've never lived in Chicago so I don't know how much the weather will be different. I don't know how your kids react to schedule changes and being out of their normal surroundings, so it's hard for me to answer.
The Washington Memorial is closed. Will be closed for a few more months as the earthquake did some damage that they are trying to fix.
I would plan on having a picnic on the National Mall and playing games there!!! Flying a kite is fun too!!!
I would also look into the Duck Tour - where you see DC from Land and water... http://www.viator.com/tours/Washington-DC/Washington-DC-D...
The Baltimore Aquarium is NOT cheap but fun for kids. Since you are driving here - I would do that as well.
Good luck!! Have fun!!!