I think not only should you charge her for the 27th but also for the half day on the 24th.
That being said, with reference to the following...
One of my DCM asked me this morning if i was open for the holidays and I answered that I was closing at noon on the 24, 25,26 are closed and I am open again on the 27th!
Did you not give notice before hand of your time off, because with only 3 working days notice for taking a half day on Xmas Eve, IMO its a bit much to expect someone to accomodate that at such short notice.

When she gave me her schedule for the month, she said that she was coming and in...
At this point I would have told her what my working schedule would be so she had at least the month of December to clear it with her employer and make her Xmas plans.

However if she is contracted to pay for all booked days regardless of change in plans, then yes she should pay for the half day. It's Xmas Eve and a lot of people finish early on this day and even more so this year as school age kids are off school. I think most people would have the ability to finish early, and honestly, you weren't giving her a choice. She has to find alternative care and that's not your problem and you are open for half a day so she should pay.

Regardless of whether or not she could get the half day finish or not, she said she was coming then said she wasn't which I agree is like trying to pull one over on you. She sould pay for sure. Seems to me like a case of poor communication.