It's certainly traumatic when my DD is terrified of someone, but I usually just remove her from the situation.
My DD is like this with the swimming teacher at the Y (unfortunately, the only teacher for her age group). Last summer, she was fine with her, but this summer, Marlena is terrified of this woman. I gave it a couple of lessons, because she loves the water so much, but it wasn't worth the terror this woman causes. Now, Marlena is so leery this woman will show up wherever she is. When we go to the public pool, she looks around warily, and asks if "Teacher" is going to be there. Basically, any time she's nervous a situation, she'll ask about "Teacher".
This makes me feel awful. All the other parents I know love the swimming instructor, so I wonder if she's violated Marlena's personal space at some time. I doubt she's a bad person.
The talk about auras is interesting to me. My DH sees them, and I wouldn't be surprised if Marlena inherited the ability.
Skim, I hope your DD doesn't encounter this woman again soon. And don't worry too much about the woman's feelings being hurt. If she's that bothered by a two-year-old's outbursts, she's just too sensitive, IMO.