I can only offer speculations as to what is going on with your mother's knee: the surgeon is the best one to understand what was done, but it sounds like there may be some scar tissue impeding her range of motion (ROM). It is natural, after surgery, for there to be a lot of swelling. That swelling can limit range of motion, but only for a while. Hopefully, after a few months when the swelling stops, the ROM comes back, but if scar tissue built up in the meantime, that can permanently reduce ROM. There is no easy way to get rid of scar tissue except through physiotherapy. Because it is tissue, with nerves and blood vessels flowing through it, it will hurt to break that tissue apart. I am not surprised that the therapy your mother is undergoing hurts.
It is unfortunate that your mother was not able to mobilize the knee soon after the surgery: that would have been the best time to reduce or even prevent the scar tissue from forming. But that is in the past: the question is - what to do now? It sounds like your doctor is saying, "The scar tissue has to be broken down, and since it is so painful, we are going to freeze this area and really get in there and break it apart." It does sound aggressive, but I can see where she is coming from. I can also understand what the physio is suggesting and why. Your main question, however, is - can this be done via Yin Yoga instead?
Maybe! I certainly see no reason to not try it. The knee needs to be mobilized and the scar tissue present there is connective tissue. Yin Yoga stresses may do some good, but I would ask the physio or doctor if they think there is any chance that Yin Yoga stresses (long held, static stresses) could possibly make matters worse. I don't think so, but they know your mother and I don't. If you are given the "all clear" signal, then start to give your mother some flexion postures that she can hold for a minute or so at a time. Work up to longer holds, and then to deeper postures.
I have to assume that there is no way your mother can currently sit on her heels, but can she sit in a chair with her knee flexed at all? When you say that she has almost no flexion, how much can she bend her knee. Whatever that range of motion is, she would need to get to that limit and stay there for a while. Hopefully, with time, that ROM will increase little by little, and she will have to continue to play the edges: stay where it is challenging. She may find that spending as much time on the floor as possible will be very beneficial. Get off chairs, if she can, and sit on the floor, on a cushion. She can sit at a coffee table to read or eat. As she sits, she can be bending her knee as much as she can, then relax it for a few minutes, then bend it again.
I wish her good luck!
ps - I would not categorize what the physiotherapist is doing as "aggressive Yin Yoga" because she is probably moving the knee, not just holding a static stress. But if holding the knee in one position for minutes at a time, and if by "aggressive" you mean holding it while pain is present, then - yes, that is a form of yin, alright.