This evening, I got some pictures of one of the fledglings feeding on a snake by itself, a couple of trees away from the nest. I am not sure if it caught the snake itself, though.
I also found this collection of feathers, part of a wing, and a claw below the nest. I think this might be an Eastern Screech Owl, but am really not sure. The patterning looks close to one I found in a feather atlas. The talon has feathering on the toes, also consistent with some sort of owl. The prey is a bit out of the ordinary for the Red-shouldered Hawk, but not unheard of according to this Wikipedia article.