You are right, in that she had seen my work and liked it and came to me. Apparently she was talking to a friend the day before she was to come and her friend said that she knew another photographer and the friend rang him for her. He said straight away that he would do the work for free.
Okay, now it's all making sense... Third parties got involved and now everything is all screwed up. Be that as it may, this woman needs to make up her mind who is doing this thing, is that the long and short of it now?
If this were me, I'd simply tell this woman what your terms are for the shoot and leave it at that. It sounds to me like your work is speaking for you. She's seen it, she been impressed by it enough to contact you to get it, now she needs to agree to your terms.
If she doesn't like your terms, or if for whatever reason she wants this other guy to do the shoot fine, I'd let her go. I'm not a professional photographer but I have been in business for myself and I never haggled with potential clients.