Ever feel floppy when you squat heavy? Do you have a massive butt wink at the bottom of the hole? Do your pull-ups feel sloppy?
Many times the most "core" issue we have with any movement is the inability to breathe effectively during that movement. We don't know how to breathe. We must learn to breathe while our core is contracted. This video talks about just that.
This is key to developing functional strength and power.