All the women in my family have furry blonde facial hair (it's politely called 'peachskin') and I was traumatised by it since aged about 8, too. "Furball" and "Ewok" were the playground insults in vogue at the time.
My mother refused to let me do anything about it (obviously because she had it, too) and so in a fit of pique I shaved my upper lip, where the hair was coarsest and most visible, with my Dad's razor. I got b*llocked, and of course it grew back darker and coarser.
As I got older, I spent a fortune on every kind of hair removal going, including depilatory cream, waxing, laser and electrolysis, and have scarred my skin as a result. Don?t touch these, by the way.
Now in my thirties, I have at last found the answer - threading. It doesn't hurt much (rub the skin to be threaded with baby oil) and isn't too expensive (£15 once a month now). It has yielded better hair growth reduction than either laser or electrolysis. Ironically, my mother has started having it done too!
Please let your daughter remove the hair. My facial hair made my school years SO miserable, and it would have been such an easy thing to fix.