I don't think "see sawing" was the right word phrase but I do understand I think what wordstoasong was saying. I think shew as saying use alternating preasure and that, done correctly won't deaden a horses mouth. She's not talking about ripping the reigns from side to side.
I'll be honost, My 24 year old qh will yank the reigns out of my hands and put his head close to the ground when he's feeling obnoxious, he's avoiding the bit and ignoring me. I'll pull him up gently, I'll do all kinds of things, in the end I'll end up yanking his head up forcefully. It's rough but it gets his attention and he will stop his antics, well... he'll move on to a differnet obnoxious tactic, but he's mr. Manners himself.
Just get her attention and keep her working.