I am sorry to learn of your mother's current diagnosis.. Mimi's suggestion was excellent and I think by the sound of your last post you have made your decision.
The truth is if she does have alzheimer's it would be good to know what stage she was in... and the rate of deterioration... you both were in NYC,,, is she frail at this time?
I am concerned if she really has a somewhat advanced stage of alz, would you just be prolonging her life.. or if the prognosis combined with the alz and the surgery is really optimistic.. many might think it would be wiser to just let her spend her time without any invasive treatments or surgeries.. and then treat her palliatively with pain meds... you might aklso want to check on the affects the anesthsia might have on your mothers Alz, blood etc. it truly is a difficult call.
I would get at least a second opinion and keep asking quetions to do what is really best for your mom.
my thoughts and prayers are with you and your mom. Research as much as you can to make the right choices...