Yeah you are probably right:') It just surprised me. It's no fun pulling a horse but I was in a position where to to back down would have let her get away with it.
I wouldn't assume she views everything as a struggle for who wins... She is probably thinking more about dinner and a nap than whether she is able to get away with a lazy lead lesson. ;~D
Hold the long whip behind you, and smack her with it, half a second after you say trot. Then start trotting as if you fully expect she's gonna do it.