Since your children are relatively young, then I would consider skipping the Capitol since it is a relatively long tour with not much interest for little ones and the US Mint is not worth the wait IMO.
If you go during a busy time, then you can skip the Washington Monument and see some great views from the tower at the Old Post Office Pavilion.
I would personally recommend:
1. The zoo (unless you already visit a great zoo frequently). The zoo is undergoing major renovations, but it still has tons to offer. The tip about getting on and off at different Metro stops is definitely the way to go.
2. Natual history museum - this can be very crowded so figure out what you really want to see. The rock and gem gallery is great and they have a very good insect area.
3. American History Museum - I haven't been after the major renovation (will probably go this spring), but they have such a mix of things that there will be something worth seeing
4. National Archives - this stop is usually left out by most, but it doesn't take long to see our most impressive documents
What to skip:
Spy museum (interesting for older children), aquarium (even newly renovated it is still bad), Holocaust museum (for older children), Air & Space (unless your dc love rockets and planes), Hirshhorn museum (modern art - good if your children appreciate that), Arlington cemetary (lots of walking, little to see), Newseum
What to consider:
Botanical gardens (can be combined with walking by the Capitol and the American Indian museum), American Indian museum (can be done quickly and they have interesting food in the cafeteria), National Gallery of Art (this has 2 wings to it so definitely decided what you want to see before you go), Iwo Jima (have the changing of the guard ceremony - I forget which day), FDR memorial, Lincoln memorial, WWII memorial (the Lincoln, WWII, and Jefferson memorials are not super close to metro stops)
Eating in the museums can be expensive, but if you go to Metro Center, Old Post Office Pavillion, or even Union Station, then you can find cheaper food.
Let me know if you have questions regarding specific attractions.
Christina