Have you seen the recordable books for kids? Most if not all of them made by Hallmark? I think an app that does that would be a huge seller.
So the app, probably for tablets and not smart phones, would allow the adult to record themselves reading a book. Then the child would pick the book, and swipe through it. There are copyright issues... So, it would probably need to be developed then sold to either hallmark or maybe ibooks?
I've got ideas for the interface, but really thats all window dressings. I think it would look nice to be able to chose a few options for customisation of a virtual books case, like color, kid's name, style of book case, and then a shelf for the books. Maybe you could sort it by reader? The grandma and grandpa, or Aunt Susie, or a family friend etc. could always be on the tablet to read a favorite book your kids.