I think that if there is a way to show her your experiences in a way that may interest her then do that. Perhaps try talk to her on her level of understanding. I know that when I was younger, (I wasn't exactly the most smart, but I've been told I'm wise beyond my years), it was very difficult for me to believe in religion because it just didn't seem to work with my very strong philosphical beliefs. It's hard for a girl at that age to accept it when she knows that kind of thing. At that age, it's mainly a burden because there's nearly no one that understands what she does so she feels by herself. I know this because I was quite unaware of this until I had a deep discussion about it with my father (agnostic). He helped me understand myself and what I was aware of.
I wouldn't say that she's smarter than you, but having that awareness of everything makes the person, in this case your grand daughter very empathetic and understanding, well it did for me. Perhaps she's stubborn about your life experiences because she feels it doesn't relate to what she knows?
Hey, and don't go and say you're not good enough, God doesn't give us challenges that we can't overcome. I found that in my own time I saw how everyone at church seemed to be happy and enjoy life, a life full of love and a strong family atmosphere. I realised that I didn't have that and the answer of why came to me. It'll take some time, but it can be done.
Good luck. :)
