Hi Muse
I guess I have just been through a similar situation, my mother needed cancer surgery and there was way she would have blood. [Interestingly the surgon wanted to know which type of JW they were, aparently there are those that will and those that won't]. The surgon repsected that they were of the "won't" variety. The medical liason committee provided some additional imformation the medical team asked for, and that was it. There was no talk at all of the medical committee being at the hospital.
Anyway the surgery went well, and they called mum wonder woman because of her rapid recovery [shes in her mid 60's].
At the end of the day any faith is just that, belief without evidence, and as such logical reasoning will not work, so you really only have one chice which is to respect your mum's choice, however nervous you may feel about it. Just let her know that you will support her as your mum no matter what her decision is.
Good luck