From the background that I've managed to piece together, Rei's mother died when she was very young. Rei has lived with her grandfather since before elementary school because her father was too busy. One fanfic I've read stated that her mother died during childbirth and her father practically abandoned her at the shrine, but I don't have all of the manga to either support or refute this. I don't know about the Anime version.

All of the information that I've gathered about Rei is derived purely from the manga, courtesy of the Mixxine pocket manga. This isn't accidental; I've purposely refrained from using the Anime as a source of info. Call it a personal reference.