Mom wants to avoid hip replacement surgery, but she hates taking pain medication for her arthritis. Any advice?

Success with any joint replacement depends on motivation and preparation.
Spinal anesthetic and heavy sedation is the way to go. As someone said you don't want to hear the saws and hammers during the surgery. There can also be considerable discomfort to the shoulder you are forced to lie on for a couple of hours for a hip. Surgery won't be successful if you don't do the rehab. It will be uncomfortable but take your pain meds half an hour before the session and it won't be too bad. Being overweight greatly reduces the chances for a successful joint replacement.
The use of narcotics for pain relief is greatly misunderstood.There is a big difference between addiction and dependence. I use the analogy of the diabetic who is dependent on Insulin. Using narcotics where there is a genuine need for the relief of pain for a short time will not cause addiction. Long term use again with the need for pain relief will cause dependence. Overtime the need to increase dosage or change the narcotic may make it necessary to increase the dosage as the patient becomes tolerant of the medication.It is very important to treat pain before it becomes intolerable as once it gets out of control it is much more difficult to relieve and may require much higher dose of the drug with the danger of side effects. It is very important to remember that any drug combination that contains Acetominophin {Tylenol} does not exceed the recommended daily dose because this may cause serious harm to the kidneys and can lead to death. If pain is out of control it may be necessary to use a more potent narcotic to regain control. Narcotics are not necessarily the first choice for pain relief. heat, ice, muscle relaxants, massage, anti seizure meds and OTCs all have their place to mention a few as with relieving other bodily problems such as infection, constipation and urinary retention. after a joint replacement swelling, stiffness, pain and some loss of blood are all normal but if the area becomes red and hot and the bodily temperature is raised along with increased pain these are all indications of infection and need immediate medical attention.
I have had a hip and knee replacement and can report excellent results. I was active before the surgery but am now active and pain free.