Mystery bird solved. A very strange situation. Yesterday we went out to look at the nest. Mommy Robin was in there so we couldn't see the babies. But I almost got nailed by the bird pictured below. It flew out and onto the house next door. Then I heard a ton of commotion from the back of the tree. I walked around and looked around and found this guy (above pic) It's a young Finch. Still has tons of fluffy feathers and I don't think it can fly yet. It just kept hopping around from branch to branch. Obviously not happy that I was there. I searched on line for "do birds share nests?" and other variations of that question and came up with nothing. So apparently the Robin doesn't care that another bird is occupying her nest along with her and her babies.
Today we got to see the babies.