After reading your description, your mother has pain when she puts her weight on that new knee===as when she climbs the stairs. She also has some trouble bending her knee---so it hurts when she sits in a low chair or when she gets up from a low chair. First I am going to tag
@Josephine our forum nurse as an advisor.
To me, I bet that she does have some problems with her patella--so that when it presses against her knee--when rising from a low chair or climbing stairs, she has some pain. In the US it is almost a standard procedure to change the patella with a small "button" of plastic which fits on the bottom of the knee cap.
Many people have pain when going up stairs or getting up from a chair which is related to arthritis under the patella. I think it is called patelleo-femoral syndrome. Obviously the patella rubs against the femoral head.
In addition, muscle weakness can also cause pain while climbing the stairs---a simple way to consider is to compare the size of the two thighs right above the knee. Even though I work out in a gym five or six days a week, my left leg is slightly smaller than my right. It is the weak leg.
You are a good son to take such care of your mother. I would ask for a second opinion of the knee from a different surgeon that you trust and also send your mom to physical therapy to have her quads (the large muscles on the thighs) evaluated. If she needs more pt, that is an inexpensive way to fix the problem.