Not sure it's off the beaten path but the National Zoo is always a winner...http://nationalzoo.si.edu/
If you are a gardener or interested in plants you might enjoy the National Arboretum. It is waaay off the beaten path, I forget how long it took to reach it by car, maybe 30 mins? I loved it. It was relatively deserted, especially after DC's lines for the attractions and all of the school groups (and early May is peak season for class trips!). There was plenty of open space where your little one could run around. ETA that the website says its 10 mins from the capital and there is public transport requiring the metrolink plus a bus, so a car would be easier.
Early May should be an ideal time there, lots of stuff should be blooming and lots of new foliage. I'm in CA so I loved seeing the many plants that we don't have out here. They have an excellent website: http://www.usna.usda.gov/index.html
Darn on that cold weather in FL, but glad you were able to get away and have happy memories too!! Nice staying right on the beach!!
My daughter & family were in DC last week during spring break and loved it. They mostly did touristy things, though, hitting all the historical spots.