I can't really judge the location of your foot plant (or, in other words, the direction of your stride) in those videos. To do so requires being able to see your feet and the pitching rubber and home plate at the same time. This is best shown in a rear view but your feet and the pitching rubber are not visible in your rear view. (I could use the hoop in your target to locate home plate.)
Your separation looks fine. However, I think you're lacking delayed shoulder rotation. In other words, your hips and shoulders seem to come around together instead of hips before shoulders. More on this later.
As for your falling off to the side, that could be caused by striding to the throwing arm side. What often happens is that an inappropriate late posture change (i.e. a bend at the waist) occurs in an attempt to get the upper half back inline with the target.
Back to the delayed shoulder rotation. If you have that late posture change, that can limit destroy the timing required to delay shoulder rotation resulting in the shoulders rotating early.
Finally, I think you are a bit off in your notion of the ball, head and foot being aligned. First, we need to be clear on when we're talking about alignment. I talk about it at release. But the alignment I look for is chin chest and front foot being aligned vertically with the ball released 8"-12" in front of the front foot. Based on this, it appears to me that your release point isn't out front as far as it could/should be. I suggest getting those hips moving forward a but sooner/faster to build more momentum and to get out over the front leg more.