Just curios, how much older is Jane to your daughter? Kids in the age group don't normally act out this way unless they are threatened. Usually this format of aggression is due to rough play.

What does your daughter say to you when asked why Jane hurts her? A question I would be asking is what did you do or say to Jane that made her bite you?

Have you asked the centre staff if your daughter is or has been aggressive in anyway? If the answer is no and no then Jane is acting out for some other reason and her parents need to get involved.