Not abusive, just plain ol stupid. I use those plastic bats to get after my dogs because they can get the reaction I want without actually hurting, and I've been known to threaten Indie with one a few times
Her attitude was all wrong though, the lady went off the handle a bit and really seems (from what I can tell in this short time frame) to be a bad trainer, or at least someone who doesn't know how to walk away before losing their temper. Her movements were choppy and messy and all over the place, she was no direct with her energy and very out of focus with the horse. Again, not abuse, just plain ol dumb.