Being a school teacher in addition to a TKD instructor, I find her behavior unacceptable. If the students could not manage the basic discipline of class (and not spitting at people is pretty basic), especially after multiple acceptable methods of discipline were tried (e.g. verbal reminders, pushups, time outs, etc), then they should not have been allowed to stay in the class. That's it.
While I understand the impulse (I've had the impulse a few times myself, teaching middle school) to tape a child's mouth, I would never do so. I know too much about the risks that accompany restricting breathing, especially in children that age, who can easily become hysterical - once they start crying, mucous would fill their noses and breathing would become difficult, if not impossible - thus, it is a health hazard, and a potentially serious one.
I am, I think, most concerned by Young's statement "I don't feel as though I did anything wrong" - potential physical complications aside, this woman chose a means of discipline that, at its root, is humiliation. This is a horrible way to teach discipline; it teaches children that humiliating someone is an acceptable response to improper behavior. That is not a lesson I would want to teach, nor do I think it would be effective in the long run.