It seems like somehow, if you feel like she trusts you, and what she says (ask her directly - do you trust me? sounds crazy but, seriously)... if you can convince her that a. you fully support her desire to compose/improvise and b. in order to get good at that, she needs to learn how to read music, or else she'll end up merely 'fiddling' with no clue as to what or how she's doing it... maybe you could get her to cooperate a little.
Have you seen the "American Popular Piano" method books? The Etudes books are designed to teach improvisation... I have yet to use them, but I have the first couple books... and we discussed them in my pedagogy class a while back - they seemed fun & interesting & modern in it's approach.
I don't know what else to say - I doubt you're a bad teacher - try having a heart-to-heart with her - ultimately, what's important is that you establish the connection so she'll trust you enough to take your direction/advise. If you can't establish that, perhaps it's just you & she don't 'click...' - but I'll bet you can find a way to connect.
You could always refuse to continue a lesson if she refuses to do any work you ask of her at all - I mean - it's a 2-way street. You say she enjoys coming to you - so use that. I have done that before - NOT in an angry way - just very matter of fact. It worked immediately both times (this was a different issue - a child who wouldn't stop fiddling/noodling - basically, listening to me - but you can modify it. Once you've had the heart2heart, just tell her, you're making a deal - and if she comes back next week having not done ANYTHING you've asked, no lesson. period.) That's what I would do - but I'm mean like that.

You do whatever you feel comfortable doing. I'm sure you can make it work!

Good luck!!