My mother is 82 and has been told to have a hip replacement ,what will happen if she chooses not to have one done and will it effect other areas of her health?

Yes it will definitely effect the other aspects of her life. She will be in pain most likely all the time, constant pain can weaken your immune system, cause mental problems, cause a patient to be on narcotics for pain control, etc. If I may ask, why does she not want to do the surgery, and what did she do to need the surgery?