As others have stated, you will definitely do a lot of walking. Considering the ages of your kids, it may be best to plan ahead on some of your stops & also to have planned stopping points to take breaks, etc. Plan to pay decent amount of $ on bottled water.
Went out with the family & my kids more than once (have family in the area). The 1 time we did the main touring thing, it was late June, hot & humid as all get out. The pictures of me at Arlington looked as though my shirt was completely soaked. Not spots, but as if I had jumped in a pool (shorts weren't that way thankfully, but pictures not the most 'pleasing' to view)
Washington monument is a must if it is open. Good to do early in the day (before 10:00 a.m. I think) as crowds building up later. All the other places posters have mentioned are great - just all depends upon taste/what would interest your kids mostly. Holocaust museum is a must at some point, but considering the ages of your kids, it may not be the best time. Just remember going the 1st time while in DC for work with some co-workers. Waited to take my kids until later so they could understand the gravity of what it is & to be ready for reactions from other people who are there. Powerful stuff to witness, much like what you man/can witness at the Viet Nam Memorial & Arlington.
Do not go to their aquarium. Unless it has changed a lot in 3-4 years, it is pretty lame.
Metro is cheap & gets to a lot of places. Keep in mind it is a subway - we were stuck in it for about 45 minutes when we were under the river. My daughter began to get a little nervous/claustrophobic during that time, but made it through just fine. Part of the adventure I suppose. Compared to other cities - it is probably one of the better run systems & definitely the cleanest.
Last but not least - I like hitting spots for food. One favorite is Ben's Chili Bowl - just off Metro stop (Q Street maybe?). Hole in the wall cafe-joint that has been show-cased on all of the food shows. Chili dogs or better yet, their Half-Smokes (type of sausage) are great.