B.L.
You might do a search on John Rosemond's site (www.rosemond.com) and see what ideas he has. He's my favorite parenting author, and I highly recommend his book Making The Terrible Twos Terrific. It probably addressed that issue in the book, but I don't remember exactly what he said. He is full of common-sense wisdom.
When my son was 2 I watched a little girl for a couple of months. He started biting her most days, and her mother finally took her somewhere else, and I couldn't blame her. He stopped once she was gone, so maybe in part he didn't like her (she was a strange child) and didn't like the competition.