J.M.
Hi L.,
You said that when you pick her up, she is having fun and a great time at school. My daughter did too and cried every morning that I dropped her off. The teachers reported that she only cried for five minutes or so and then was fine. One day gramma dropped her off and she didn't cry. When gramma asked why, she said, "I only cry for my mommma." I didn't worry after that.
Also, my daughter just started kindergarten which is more structured than her free-choice preschool. It was a difficult transition and took 4-6 weeks for her to acclimate.
If you're sure that this is the preschool for her, my advice is to ignore her when she's fussing about school. Things like, "I really want to read you a bedtime story. I can't until you're happy." This worked with both of my kids (we still do it with my son). In her own way, she's telling you how much she loves you...
Good luck.