The first video shows us just getting started and the second involves a longer portion of the lesson. The sound quality is excellent, so I'll let Chemaine speak for herself. Please ignore my attempts at commenting. I am very much an auditory learner (hearing myself explain it back really helps), and I need mechanical explanations. You'll hear me trying to articulate what I am struggling with or feeling so that I can get that mechanical explanation that I need.
By allowing my legs to swing forward and back, my hips and legs got looser and softer. Conversely, by restricting that swing, I could collect Speedy's canter. It felt more dramatic in person, but you can see it a bit in the video.
At first, she asked me to ride without swinging my legs so that I could feel how much looser I had gotten over the course of the lesson. Then, she asked me to swing my legs with the canter to feel the difference. See if you can spot the difference.