I had my left knee replaced five years ago. I learned that PT was not to be used to heal me, it was intended to see how well I had healed myself. The exercises they give are important to be done diligently. I did that, and after about four weeks of twice a week appointments, they said I was progressed beyond what they could teach me, and they turned me loose. I was back to work with full motion about six weeks after surgery.
One of the primary things I did during my recovery at home was to try and improve flexibility of the new joint. As things heal, if the joint isn't flexed enough, developing scar tissue can restrict movement, and the knee won't be as flexible. This is hard to describe, so try and picture it: What I did was lay on my back on my bed or sofa. I'd flex my (new knee) leg at the hip, raising my foot up in the air, straight up, with my leg straight, and knee not bent. Then I'd lace my fingers around the back of my thigh, close to the knee, to support my upper leg. Then I'd relax the lower leg, and let my foot slowly drop, bit by bit, to see how low it would go. I'd find a point on the wall to use as a visual reference, to see how low my foot would drop. When I got as far down as it would go, I'd straighten my leg again and repeat the motion, several times. I did this several times every day, and before I knew it, my foot was nearly down to the top of the mattress. The surgeon was trying to get about 115-120 degrees of flex in the knee, and I got more than 130 degrees. We were both very pleased.
The other thing was to take daily walks several times a day, even short ones, to improve stability. I did laps around the interior of my house, slowly, and at my own pace. I started wth a walker (no crutches), then graduated to a cane, then to my outstretched hands. I was never far from something to catch myself if I felt myself slipping, and I didn't fall. I got better very quickly.
The other thing was that walker - I used one in the shower. It gave me support where I was most vulnerable, and made showering a lot easier.
I came through my surgery pretty easily, and I was very glad I did it. The chronic arthritis I'd dealt with for 30+ years was gone, instantly. The pain I did have after surgery was soft tissue muscle pain, not bone-on-bone arthritis pain. And for that, I was immediately grateful.
One thing to understand: If they save and refurbish your kneecap, as they did for me, know that you will not be able to kneel down on it. The term "get down on your hands and knees" turns you into a tripod, because you will not be able to kneel on the new knee. To try and kneel on the surgical knee, putting pressure on the original kneecap with the artificial joint behind it, creates a pain so excruciating, it will bring instant tears to your eyes. Horrific pain, at least in my case. My surgeon didn't tell me that would be the case. Also, that I wouldn't be able to run any more, because they didn't want me to put that much pounding pressure on the new joint. I can fast-walk, and lightly jog for short distances, but long distance running is a thing of the past.
Good luck with things. Let me know if you have any questions.
Dave