I believe there are a number of programs that can track your work by the minute - check in Time Management or use the forum search feature to see if you can find those conversations (I'm sorry I can't recall exactly where they are...) Also, I'm sure someone else will jump in here and post their two cents and may have some insight about the time tracking software.
I work in the same manner you do and have not ever used any software for tracking my time. I think you could try explaining to her the way in which you work/invoice and let her know that if she'd like to receive daily reports in the manner she's requesting you'd be happy to set up a program of her choice at her expense (unless you were planning on incorporating it into your practice anyway). People may disagree with me on this but I feel that as a business owner it is up to you to delineate what it is you offer and in what manner - anything beyond that at a client's request will be passed on to the client in terms of cost, etc.
I hope that helps!

You're right that you're not an employee and if you're starting to feel that your own policies are being impinged upon do what you can to help (gently) steer the client back into line with what works for you.