Lower Back "Plop!" When Squatting, Still Stiff

I actually have that same problem caused by a congenital defect. My right leg is “longer” than my left because of the hip misalignment.

A stiff muscle is not necessarily a strong muscle, it’s simply being overworked. It is compensating for a structural issue. Definitely work on abdominal strength. Since I’m lazy and don’t feel like typing it again, here’s a link to a post I did regarding this: