Every major surgery carries some risks and complications for patients including complications arising from anesthesia. Your grandmother's advancing age and any other co- morbid diseases like diabetes or hypertension may carry some chances of intra operative or post operative complications. Spinal surgery carries its own complications as the surgical procedure is done close to the spinal cord which carries all the nerves to the body from brain. Some of these risks and complications can be avoided with skill and efficiency of the performing surgeon. So, it falls within the rights of the patient to deny a doctor from performing surgery if he or she is not confident or comfortable with the doctor.
Detailed informed consent from the patient (or from spouse, next of kin or relative, if the patient is not in a physical/mental condition to take decision) is absolutely necessary before the surgeon can perform any surgery on the patient. No hospital or doctor can deny the patient from taking a second opinion from another doctor if she is not happy with her present consultant or hospital. You can find another neurosurgeon with whom the patient is comfortable and confident before opting for surgery.
Hope this helps. Do get back to with any further questions. Thank you