You are her supervisor? That's good, because you are on your way up somewhere in the world. As you go up in the corporate ranks, you'll be getting all sorts of unfortunate language slung at you, some of it intentional and some of not. In almost every case, I doubt that the correct reaction is for you to retreat into your shell, wall yourself in there and refuse to have anything further to do with the world at large. You are not going to make it further up the ranks if you are reacting this way every time somebody says something to you that you don't like.
For one thing, if you have a formal role as her supervisor, you have far more options than what you are doing. One of these options is to ask her why she thinks your approach is "hit and miss" and what approach does she have in mind instead?
Sometimes, lightning strikes, wisdom comes out of the mouth of children and by George, she is right! Or more likely, lightning didn't strike and as you query further and further into what she is has in mind, she has nothing but hot air to back it up and she fizzles under your inquiry. If someone thinks they have a better approach than mine, I'd certainly want to know about it.
You need to develop a thicker skin because as you go up in the management ranks, you'll be getting all sorts of stuff slung at you, some of it justified, some not. Learning how to take it and how to react to it is an essential part of your toolkit. On the job as well as in life.
I'll note that as her supervisor, your task is to train her. You are not anywhere close to finishing your task. I trust that you are not training her out of the goodness of your heart but because your organization requires you to do it so that she can perform her role. And until you have fully trained her, you haven't performed your task.
Ignoring her e-mails amounts to going into a sulk. Seven year olds go into a sulk. You are no longer seven years old. Finish your task of training her, and the sooner and the more thoroughly you do it, the more effectively she will be out of your hair. Not finishing the task of training her is not an option. You are expected to do it. Do it. You can't let a couple of loser remarks stop you and what you have to do stop you dead in your tracks - that would be just too easy.
If sergeants stopped training recruits every time recruits mouth off at them, there wouldn't be any armed forces any more. You are her sergeant, she is your recruit and your task as a sergeant is not finished until your recruit is trained. So, get your task done by whatever means necessary including telling her to stifle it if that's what you have to tell her. I'll tell you this much, going into a sulk is NOT how you exercise authority as a supervisor. Or as a manager. Or as the CEO. And especially not as a parent :)
