It's kind of tempting to say that Mom is the protagonist here because she takes up most of the text, but there are two crucial points that make Girl the protagonist. First, the title: not "Mother," or "Mother and Daughter," but "Girl." The title character is usually a pretty good bet for the protagonist.
Second, the girl uses "I" when she talks. This puts us in the position of seeing through her eyes and hearing Mom through her ears. Since that makes it Girl's story, she's our protagonist all right.