Thanks everyone for taking the time to respond. This little girl's mom actually first mentioned it to me that she was seeing the behavior at home (her 2 older sisters developed the same attitude, but at not quite early an age). Mom was wondering if I was seeing the behavior here as well. I was not, at the time. However, about 2 weeks ago a tantrum started in the car with Mom over what shoes she had wanted to wear. Mom could not calm her (there is nothing that will calm this child; you just have to put her somewhere safe and let her calm herself down). We were all playing outside at the time and I took the child in my arms so poor Mom could go to work. Once she kicked me, I then restrained her in a wagon that I had handy and let her scream it out. Lovely scene for the neighbors @ 7:30am
So, since then, usually once a day (almost always within the first hour of arrival) this child has a similar tantrum when she does not get what she wants (toy). That, of course, does not fly here. At first I would be very stern, sit her in the timeout chair. Every time I would look at her (say "are you calm now?"), she would start again. Now, I've created a pillow for her. As soon as I see her getting frustrated she now goes straight to her pillow and gets up when she's calm. I'm happy with this resolution as it has taught her to deal with her own emotions and she is getting no reinforcement from me (audience for her tantrum).