You ask a very good question. Researchers are always looking for ways to predict results for various diseases or surgeries. In the case of a total knee replacement (TKR), pain, stiffness, and physical function before surgery can be measured. There's a specific test called the WOMAC Arthritis Index that may be helpful.
Patients who get a low score (meaning poor health) often have the worst results after TKR. Patients with scores that show good to excellent health have the best results.
Your doctor is right though. Even if the test predicts a poor outcome, the final decision is the patient's. Counseling may be helpful if there is a psychologic reason for your mother-in-law's behavior. You may want to bring this idea up to the doctor if you can't discuss it directly with the patient.