Yes but she also works independently via AW and her own site. As far as I'm aware you booked her directly and she missed your appointment. The agency didn't handle your booking.
So she treats punters better if they book through your agency?
How do you ensure that? Have you any evidence to demonstrate that?
My experience has been that once a lying cheating timewater, always a lying cheating timewaster. A dalmatian dog does not change its spots. You have her on your books.
Her actions reflect on you, whether she was booked through you is not material. Now if I was asking for compensation, I could understand your point that I may have booked her through AW. But this is about her reputation and it doesnt matter whether the booking was through the agency or direct, it impacts on her reputation and by association, on your agencies reputation.
You will have to do better than simply posting as glib comment that my posting was misleading.