I went up on Sunday and parked near the Rosslyn Metro stop and rode that in - I didn’t run into much traffic at all. It’s a bit of a walk from the Smithsonian stop to the tidal basin but not too bad. It was busy, I’d say there were hundreds of thousands of people there, but it wasn’t overly crowded.
Pro tip: don’t bother with a stroller. If you have a backpack carrier for your 2 year old that would be perfect. It gets really muddy at the tidal basin and with all the crowds everything from crossing the street to navigating over tree roots will be a challenge if your kids in a stroller. Also wear waterproof shoes and bring a change of clothes (or 2) for the kid. And bring extra water - the concession lines looked very long.