I am asking about my 82 year old Mom who is having serious mobility issues. My Mom lives at home with my brother. Any ideas?

Andrea, I am supposing that Mom has had xrays of the knee. Do they show arthritis? This sort of wobbling jello feel is what is commonly felt, as though the knees will not "hold" you, as though they are unsafe and wobbling when weight is put on them. It then becomes a somewhat vicious circle of the knees affecting the balance and vice versa. Was Mom initially a bit better, then worse? Did she have rehab after her surgery?
Aging is just so tricky with the extremities. Giving you a for instance, when I am on the bus now, standing on a moving bus holding on, the arthritic knees can feel like they are nothing, and my entire body feels like a feather in the wind, falling forward and back in a way it never did. I have to laugh because it feels as though I am lighter, and just floating about, when in fact I weigh easily 15 pounds over what I weighed at 50 when my stance was firm and strong.
Ask the doctor for an orthopedic consult. Get those knee xrays. Ask for a physical therapy consult for some gentle strengthening exercises. But after all THAT is done and said, Mom may be where I am, and in fact a few years further on than me. We come to feel like a candle in the wind.

It sounds as though her knees are very arthritic which is and can be common certainly for her age. My husband had knee surgery and still has issues. He is 71. He feels he cannot have knee replacement as he has other health issues. It doesn't sound as though your mother had knee replacement although you didn't indicate if she did. I think perhaps your mother should see a good orthopedic doctor who specializes ideally with geriatric patients. There are injection which might help. She certainly should continue to rely on her walker. My mother is always with hers. She has problems with just about every part of her body and is immobile to a degree. I am sure others will offer advice. I hope you find the proper care for her.