This is an update and although it would sometimes still move a little, it's much better. With time it should be perfectly unnoticeable.
Thanks again! I printed your comments and put them in my riding journal.
The video also has me cantering so feel free to comment on that too. In the end I sort of lost control, as in, I did something and Coco seemed to understand that I wanted to stop, when I didn't... or she decided she would stop and saw an easy way out of it. Maybe someone will notice what I did wrong.