I also suffer from this but it started when I was ten years old. It's called trichotillomania.
Here is a resource site for more information:
http://www.trich.org/
I've been to five different psycologists and psycothereapists and on multiple different forms of drugs but nothing worked except for learning to control my stress triggers. I pull when I'm stressed. It's a cliché. You see cartoon characters drawn ripping out their hair when they get frustrated and that's the way I feel.
Some people have trich worse than others. Everyone is different. Like your daughter I pretty much have always pulled from my face but there was a brief period of time when I was in high school, and forced to stand up in front of the class to give presentations on school projects when I started ripping out patches from my scalp to the point where I looked like I had mange.
As an adult I have better control over my stressors and can politely turn down invitations to events that will stress me out so I can save my hair but it's so hard because it takes six months for eyebrows to grow back fully and longer for eyelashes. So one bad episode of pulling can undo over half a years growth. It's disheartening.
I would grow it all back and be in a happy place and then something would happen to trigger an attack and I'd be morose and depressed for weeks afterwards, removing myself from the world so I wouldn't have to face anyone with my non-face.
It's a hard thing to deal with but what made it worse was that my parents thought something was terribly wrong with me and it tore me up with how much they tried to "fix" me when doctors said there is no "cure". I just needed to learn to manage my stress to prevent an attack. But they didn't like that answer so they tore me up dragging me from place to place and experimenting to try and fix it.
Trich has only been "discovered" for about the last twenty years, and twenty one years ago was when I first started pulling so the resources were thin to nonexistent back then. I haven't explored new treatment since my last visit with a doctor about fifteen years ago so who knows, what they know about this problem could have advanced with leaps and bounds for all I know. I haven't had the courage to go and find out. I've just accepted that this is part of who I am.
One thing stuck in my head growing up though. One day when I was fixing my hair in the mirror before going out with my family to the aquarium or someplace. I was getting frustrated that my long hair wasn't staying properly in the banana clip I was trying to do it up in. Apparently I was holding up the whole family because everyone else was in the car and my dad was standing by the front door waiting for me to exit so he could lock it. He called out and told me to hurry up and asked what was taking so long. I told him I was trying to fix my hair and I'd be right there. Then he yelled, "You have no hair on your face, who the hell is going to give a damn about the hair on your head."
My heart just fell into my stomach. I knew he was frustrated at how I was holding everyone up but it colored how I looked at myself from then on. I sort of gave up trying to look pretty. I'd look in the mirror when trying to get ready to go out and just give up and leave my hair down. I grew out my bangs so they fell into my eyes and would sometimes poke my iris because I had no lashes to protect them. I took to wearing sunglasses a lot.
I only bare my soul to you now to help you understand that your daughter can't help what she's doing and will hate herself every time she pulls. It's a vicious thing. And she will take any admonishments about what she's doing to heart and hold onto them forever.
Once my mother tried to get me to stop by recruiting my uncle to tell me that if I didn't stop pulling my eyelashes and eyebrows out, I wouldn't be allowed to go to summer camp with his family that summer. I was so stressed about not pulling so I could go to camp that it triggered an attack and I destroyed my face again. I was mortified and devastated. I just wanted to give up and quit life sometimes. I felt like I was playing a rigged game.
I've never tried hypnotism but that's because I think it's bunk and wouldn't work on me. You need to believe in it and want it to work for it to do any good.
I'm 32 and I've been pulling since the fifth grade. The longest period of time I went pull free was two years and three months. One of my worst memories about this was when this problem first manifested and one day I went to school and was fine and in two days I had no eyebrows or eyelashes and the kids in my class noticed. They noticed and one loud obnoxious boy drew attention to me by yelling, "HEY! NICOLE SHAVED HER EYEBROWS!" So of course everyone crouded around me and mortified I bolted from the classroom and hid in the boys bathroom. I would have hid in the girls bathroom but I knew they'd never look for me in the boys so I stayed there for the rest of the school day in a gross boy stall. When I emerged after the last bell to run to my mother's waiting car the car was parked in the lot but my mother wasn't there. I got snagged by one of the teachers and brought to the principles office where my mother and my teacher were waiting for me. I had to explain, to these adults, where I was, why I left and what set me off. It was insult to injury.
Since then I hid in a lot of bathrooms to avoid things like having to give presentations in front of the class. I would work diligently on my projects doing A+ work on them but I would skip the day for presenting by hiding and then turn in the project a day late, always to receive a zero for not presenting. I had a teacher tell me she really wanted to give me the A I deserved but she just didn't understand why I wouldn't get up in front of the class to finish the assignment properly.
I chose the bad grade over the mortification.