My leg swings back when I canter. Almost like a back and fourth motion. And I do put my heals down, how do I keep this from happening?!

Put more weight in your feet, not necessarily putting your heels down more just keeping your balance in your toes
Tie your stirrups to the girth
Agree wo
Stand up in stirrup
Lots and lots of no stirrup!! It builds your leg muscles and then your muscles naturally learn to grip and not swing!
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