When I twist my hips, my knee bends inward... help?
OK I'm only green belt TKD so I'm no expert, but I'll try to help until someone else steps in.
When you say your 'knee bends in' I think you mean your lower leg, right?
Obviously you do the hip movement after your foot has left the ground. Your knee will naturally bend in a little bit, that's what you want. If you watch the clip again, his leg is not fully straight when he connects. If it was, you would not have the same momentum (power) on impact.
Just concentrate on rotating on your balancing foot and torque on your hips, the rest will come naturally. :-)