Thanks everyone for your responses. They were all very helpful.
Bob, six weeks later I am rereading this thread and realizing that you had my student pegged even before I did. Her mom was her previous teacher, and I think there indeed has been pressure put on her to do well with the piano from a very young age.
I loved your idea of having her compose and write out the notes! I had her choose a Christmas song she wanted to learn and told her to sound out the melody with her right hand. She came back the next week so excited that she had done it. I was impressed - it was very good. Next week, we're going to write out the notes. She has been learning about I, V, and V7, so I'll have her use those basic chords she knows to provide a simple accompaniment to her melody.
She doesn't push my hand away anymore, thank goodness. I am patient with her, but insistent. I expect her to use consistent fingering and I won't move on to the next part until she plays it correctly.
I have also come to realize that her sighreading is really good in both clefs from C to G (would that be considered C position?), but she struggles with the notes in between. We are working on those. At least I have a better idea of what I can expect her to be able to do when it comes to reading music.
Anyway, there's a little update. Thanks again for your ideas and input!