To update what I wrote...yesterday my mare got very excited about a canter and did NOT want to listen. At a minimum, she wanted a fast trot to join with our Appy a couple hundred yards ahead (ridden by my youngest daughter) and to home. It was a fight to get her to walk, so I compromised: she could walk to
the Appy, or trot away
from the gelding. She got to choose the speed, but I got to choose the direction. It went on for at least 5 minutes, and felt like longer, but in the end she decided going to
the other horse was more important than trotting
to the other horse. For the rest of the ride, she was a sweetheart.
And the Appy? Good ol' Trooper just stood there, looking slightly puzzled at our antics but willing to wait until we got things sorted out. Not sure if I handled it right, but it seemed to work out OK.
There is a difference between a horse saying, "A trot would be fun now" and a horse saying, "I'll trot (or canter, or gallop) if I want to!"