This is only my very limited experience talking, but it may speak to your situation:
DS3 loves books. Really loves them. And he also LOVES to be read to. I find that when it is a story he has heard or read before, he is a lot less likely to want to be the "reader", preferring to snuggle up and have me read to him. When using a familiar book, I get him to read by taking turns...I read one page, then he reads the next. We read as a team.
In fact, my mother is a literacy specialist and gave me some books designed for this very thing. They are called We Both Read books and they are designed with parts for parents to read and parts for the kids. Link is here:
We Both Read book series If I really want him to read all by himself, I go to the library (just did this last night) and get some new books. He cannot resist new books. I tell him he can read his new books, but I won't be reading with him until he reads on his own. Works like a charm every time.
That's what we do in my house and both methods really work to get him reading on his own. But the "buttons" to push on each kid are so different that I don't know if these same things will work for your daughter. Just some suggestions.
Good luck!
