These types of guests are tricky. Is she entitled (or deserving) to a refund? No. After all, her only excuse for cancelling was, she wouldn't 'need' it. It is all about her. To her a booking appears to be no more than a 'placeholder'; to you, of course, it is income.
She is a discounter, always looking for a bargain, so it may be plausible that she found a cheaper place, after all, your welfare is low on her list of considerations. Also there is the dimension of a bad review, so count on a less-than-stellar review if she doesn't get her way; however those types of 'revenge' reviews are easy to cut down to size and make you look good in the process, or even removed if handled well.
May I suggest (in essence) this: 'A pity you are unable to stay the second night you booked. ~IF~ I end up re-booking the day you wouldn't be able to stay, I will be glad to refund you for that night. Given it's such a short notice the chances are slim, but you never know".
Let the whining on her part begin. 🙂