I'm not the parent, but I can almost do the Asian squat. If I have shoes with a heal, or I'm on a slight downward slope, it's not much of a problem. I can get way past horizontal and hold it for quite a long time (very useful when gardening).

I can tell you that there should be no stress in your knees at all. The feet should be pointing about 30 degrees outside of center and your knees should be pointing in the exact same direction. Your ACL doesn't get involved at all, and if it does, either your knees are going outside of the plane from where your legs are pointing, or you are having problems with balance, or you have some other structural problem in your legs.

Now, there are a couple of key points. I am Caucasian and grew up in Canada, but have lived in Japan for more than 10 years. I can sit in seiza (formal kneeling position) for something like an hour. This means that I can kneel down, extend my feet (so that the tops are flat on the floor) and sit back so that I'm sitting on my own heels. This requires very good flexibility in the quadriceps. To do the "asian squat", you need to be able to do that, otherwise you won't be able to bring your bum down to your heels. Because you are heavy, if your quads are not loose, you can stress the insertion points around the knee. It is possible that when you were practicing, you were getting discomfort there, which caused you to move your knees out of the correct plane. It took me years to work up to where sitting seiza is a comfortable and normal position for me (and oddly, I'm happier in seiza than I am cross legged). We don't have chairs in my house, and I eat all my meals in seiza :-)

Another thing is that unless you have insane ankle flexibility, you have to keep your legs apart (again facing out to the sides about 30 degrees) and lower your torso between your legs. That's because there is a fairly large moment due to much of your mass being around your chest and shoulders. You have to bring that forward of your centre of gravity, but if you keep your legs together and your feet pointing forward, then the only way to do it is to lower your knees towards your feet. If you've got great ankle flexibility it can be done, but most people can't do that (even those that can easily do the "asian squat").

Finally, as I've said, you need to have good flexibility in your ankles. For me, that's the limiting factor (broke my ankles a few times playing soccer when I was young). But it's worth working up that flexibility because it will pay off when you are older. It's one of the first thing that stops people being able to walk because they can't handle uneven surfaces due to lack of flexibility.

I'm really sorry that you injured your knee. I also think it's unlikely that the training you did for squats was the direct cause. Ligaments don't work that way. If you stretched them funny, you would end up with a dislocated knee, not a torn ACL (talk to literally any woman who trained gymnastics seriously as a child -- virtually every single one of them dislocates their knees at the drop of the hat). It is, however, possible (in my mind, anyway) that you injured your knees in the training and this caused you to overcompensate somewhere and land awkwardly. I think your warning is well taken because it is an extreme position and you should be careful when working up to that kind of thing.