IME the interstates are pretty easy-going on the weekends, but some surface streets can be slower-going. By late afternoon/early evening Sunday the traffic flowing back into the city and surrounding areas starts to thicken.
Like PP said, what route are you taking?
There are parks all over the place. We live just north of Bethesda, so Montgomery Co, and there are parks in every direction -- small, medium and large.
The regional parks are really awesome -- there's one in Wheaton that all my children love. There's another one probably too far northwest of what you're talking, Cabin John, that is my favorite.
But there are neighborhood parks everywhere and that could be a good opportunity for your child to get out the 'wiggles.' My youngest is 21 months...so I definately understand that need.