I've been riding twice as long as halfpassgal's been alive, and wish I had half the velcro-seat she does. When I work with horses who were messed up by ignorance and/or arrogance, I make sure I've stacked the deck way more in my favor before ever getting on them.
Even so, like the mare in the first video, sometimes they flash back to past bad memories and revert to old behaviors they developed way back when to save themselves. When that happens, the only way out is through. You have to stay on, stay calm, not punish, and straighten things out.
No funky sticks, magic ropes, waving flags, or endless circling. Just good classic horsemanship, pure and simple. As the late Col. Alois Podhajsky said, "Riding forward is the essence of correct training."
Calm, straight, and forward beats all those funky sticks, magic ropes, and round-penning ad-nauseam every time.