Honestly, there is a lot that you could do for free, so I would probably skip some of the museums that charge entrance fees since it'll be a relatively short trip. I also highly recommend using public transportation or Uber because driving in the city is not for the faint of heart. My personal recommendations would be to spend one day at the zoo, and the rest of the time down by the Mall. Air and Space is such a fun museum! I also really love American History, but my DH prefers Natural History. Both are worth checking out. I haven't been to the newest of the museums (American Indian or African American), but I've heard that they're both really nice. There are also several art galleries that may or may not interest your family. There's a sculpture garden on the mall that has a bunch of fun abstract/whimsical pieces, and might be a good place to let off some steam. Other people have also mentioned some of the tours that are offered, such as the Capital building.
Personally, I would skip the Newseum unless you really, really, really like reading. I've been twice and both times I thought it was interesting, but not interesting enough to justify the expense.
Unfortunately, the Washington Monument will be closed until Spring of 2019, but it can be fun to walk around and explore the other monuments. The war memorials are beautiful and very moving, especially the Vietnam memorial. There are also several tour bus companies that run in the area, generally out of Union Station, which is a nice way to get oriented.
Just two things to keep in mind: 1) DC is a relatively small city. If your family doesn't mind walking a little bit, it can often be faster to walk than Metro, especially if you need to switch trains. For example, if you were trying to get from the Smithsonian station to the Archives/Navy Memorial/Penn Quarter station, it might be faster to walk. 2) To get into the Smithsonian museums, you have to go through security. They have a whole list of prohibited things, including pocket knives. DH occasionally forgets this, and had to leave his pocket knife hidden under a giant planter on the sidewalk once because we didn't have our car nearby and he didn't want it to get confiscated. (It actually was still there when we returned to retrieve it!)