You appear to be lacking some mobility of being able to get your butt down without leaning way forward. Your back flattens to much.  your wide stance video looks better than regular, but I think lack of flexibility and mobility is still an issue.  You should have a feeling of sitting “back” in a squat.  It might help to place a box/chair, etc.. below your butt, so that when you squat down, your butt makes contact with the object at a point your legs are parallel to the ground. Try to sit down on it, then press yourself back up. 

Also, back squat and front squat work different muscles, to a degree.  A low bar back squat, for example, uses glutes, hamstrings, hips and some quads. The front squat is much more quad focused because of how upright you are.