We have two daughters who are now 11 and 8, very active, love the outdoors and most anything that is "nature" involved.
1. They LOVE Point Lookout, Md, which is about an hour outside the DC Metro. There are lakes, the Chesapeake Bay, Potomac River to swim in, a great, active nature center with a Jr. Ranger Program (check the dates), lots of trails, canoes and kayaks to rent, bike paths, a fishing pier, crabbing areas, etc.
2. Hershey Park is a great place for kids and ours really enjoyed it. We did a day in the park, took a day to just lay around (it was raining) and then did another day at the park. Worked well, nobody was too tired.
3. Jellystone in Luray, VA has so many activities within the park, then there is also Luray Caverns that youngsters definitely would enjoy.
4. Virginia State Parks has many parks in the area that might meet your requirements - there is
a. Mason Neck SP
b. Leesylvania
c. Sky Meadows
d. Shenandoah River
e. Caledon
f. Westmoreland
g. Lake Anna
If you just look up Va State Parks, you can click on either of these to see what they offer. Many offer pools, bike trails, hiking, bird watching and horseback riding.
Just a few of my thoughts within a couple of hours of DC.