if parents are reading a book to their daughter but hate it because they've read it 100 times already, but since she is young and wants to hear it again and she is their daughter: they are reading the book for the girl's sake. (For example)
I still wouldn't say it's for "her sake." I would say "because she wants it" or something else. For me "for her sake" seems like "the devil will come and possess her if we don't read this book", with a bit of exaggeration.