Emmy and the Incredible Shrinking Rat by Lynne Jonell

Emmy Addison was perfectly happy as the daughter of bookstore owners—and then her parents inherited a lot of money and she suddenly became invisible. She can't understand why her formerly attentive and loving mother and father keep taking off for faraway places and leaving her in the hands of an incredibly controlling nanny named Miss Barmy. And no one at school seems to know she exists. Then, she is bitten by the classroom rat and discovers that she can understand every word he says, as can Joe, one of the cool kids in her class who was also bitten. At this point, events start to unfold and a fast-paced adventure begins. To Joe's chagrin, he discovers that a second bite makes a person shrink to the size of an action figure and Emmy discovers that Miss Barmy has been mixing animal essences together to control the Addisons' lives. With the aid of new animal friends, Emmy embarks upon a perilous path to undo the evil nanny's sinister plans.