About the only time you could visit both parks in the same day is near the July 4th holiday when SWF stays open until 10pm. In that case, we stayed at the Renaissance resort across the street. We left DC at about 5pm, went to the Renaissance, changed cloths, and went to SWF to watch the fireworks show.
When you leave DC, you'll be tired. It's an all day experience.
Your DC badge gets you 7 days at SWF, so you'll want to take advantage of that and visit a couple times.