Sure, if she's sound, let her work. Keep her going slow and correct, but by all means, let her go every now and then. Nothing pisses my mare off more than binding her up going slow. When she gets stiff and tight like that, I push her hard and make her run out. She gets super happy doing that. I don't accept crazy behavior, but if she gets stuck sometimes that's what she needs. You just have to know your horse. If you think your horse will get too crazy doing this, then don't. If you think it'll help, go for it.
Bend is your friend on a hot barrel horse. Ride her like a reiner. Hot horses get tight and stiffen up. Make her drive into the bridle, and get her soft in the face (As a WP horse I'm sure she is already) and bend her almost to your boot going to that barrel going slow.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.