I don't mean to assume this, but it would seem to me that there are certain ideas, or certain experiences written about in the book, that are what you want to talk to her about. Why not go through the book and highlight those, and either read her the passages or summarize the things you want to talk further about?

Reading 10 minutes of a book may not be enough of a "chunk" to have what's written there make much sense. I don't know the book, I am just assuming again based on my experience of reading books to and with my older children (e.g. those who read). When we read The Hunger Games, for example, we read for 45minutes at a time. But that was fiction and you are talking about a nonfiction book (I think).

Plus, given the way you set this up, it seems a bit like perhaps you are trying to force her into reading the book when she doesn't really want to. I suppose there is nothing wrong with you asking and nothing wrong with her doing it if you do, but I wonder if it will really serve your needs. If what you want is for her to know what parts of the book you resonate with, it makes more sense (to me, I realize this may not be what you want or need) to read or summarize those passages and ask her to engage in those further with you.