Ok so here's the thing... relative or not, she is charging you and in the absence of a contract you do not legally have to pay her for Christmas Day.
I would play it a bit simple, act surprised and ask her why she is expecting you to pay her for a day that she will not be minding your child.
See what her reasoning is. If she starts waffling about bank holidays etc. Just gently remind her that A) she's never minded DC on bank holidays and in the absence of a contract you are neither legally nor duty bound to pay her anything and suggest a contract that makes you both happy going forward.
I strongly suspect she is chancing her arm and that's rather cheeky.
I also suspect it will become a bone of contention between you but there's no easy way around this, you're going to have to deal with her and you need to do it face to face.
Can we assume you pay her less than a registered child minder?
I had this problem: my friend "offered" to mind my child while I was at work 2 days a week which I thought was unbelievably generous and then slapped me with an hourly rate and all kinds of outrageous demands so I told her thanks but no thanks and went to a proper child minder.
It's difficult but you've both dug yourselves a hole here so you both need a face to face and acknowledge it and then make a plan for the new year.
Good luck. Xx