Fred Stays with Me! by Nancy Coffelt, illustrated by Tricia Tusa.
In this book, a little girl moves between her father and her mother, but Fred her dog moves with her to both homes. She explains the differences between the two homes in terms of her bedroom and what Fred does. But both of her parents are getting tired of Fred and all of the messes and problems he creates. Neither of them want the dog to stay with them, but the little girl has the solution.
This is a lovely book on divorce. It is handled matter-of-factly, rather than as a disaster for a child. I love the girl and her spunk that she obviously gets from Fred. The text is very brief and many of the illustrations will have people giggling, especially when Fred barks at the poodle next door.
Usually I am not one for bibliotherapy books, but this one would be nice to give to children going through a divorce. Otherwise, it is a good read no matter what sort of family you live in, especially a family of dog lovers.