This is actually the best advice in this thread.
Odds are flexibility is only a small part of the problem. Amongst other things, strength and proprioception seem to be bigger issues.
I'd strongly suggest you try a less than body weight squat by holding onto something for support and getting as low as you can, even if you need to lean away and "hang" off the support. Sort of like this:
https://www.youtube.com/watch?featur...CWv8UPAI#t=77s
You can use that position as a slow stretch too, to sort of feel out where things are tight, and where it's just a balance/strength/proprioception issue.
Actually, I'd really like to see a video of you doing both - sitting in a below parallel chair as others suggest, and trying the "holding onto something" squat.