Front hip opens...stretch created between upper and lower body.....stretch and fire launch.
Your 'hips stay square' is simply not done. And has nothing to do with hitting the outside pitch. The lead leg/hip must get out of the way so the swing can be executed.
You have at least one thing right....the rear hip/leg/knee action is very important. In fact, watch the rear hip come up and through as your rear knee goes to the ball. This hip action can not happen unless there is 1) a good load in the rear hip and 2) the lead leg/hip has gotten out of the way.
For you to understand the swing you have to first recognize/determine the 'go' frame....and the position they are in at 'go'.....the position from which they launch...their position at commitment.
Then watch the frames before 'go'. You will see the loading/opening of the lower body against the closed upper body.
It amazes me how people will teach separation in throwing but avoid it in hitting. They are quite sure the shoulders back and the hips open is THE way in throwing yet insist that the hip must stay closed....that the hitter must stay square.....in hitting.
You have all the time you need (with practice) to learn how to use the 'wait' time to get yourself loaded/separated.....so that you can launch and spend immediately at 'go'.
An absolute for the quickest launch possible is separation.....stretch between the upper and lower body. You can not separate AND keep the hips square.
Square is not bad.....it's just it's the upper body/shoulders that has to remain square....not the lower body.