Totally agree with spar. I found that lower lumbar tightness along with shoving the femurs apart very hard were key to keeping the knees in position. I also have a couple of other observations:
1) Are you trying to squat low bar? It's hard to tell, but from the first video, the bar looks too high. This will force you to have a more vertical back angle and the knees will want to come forward more, and it looks like you are trying to "sit back". That's going to make it VERY hard to keep your lumbar tight.
2) I guess you were probably trying to stay tighter in the second video, because did you notice they were above parallel, whereas the first one was to depth?
Make sure you're doing
low bar.