"I don't know if i approve of this, what would you do if your daughter got this haircut?"
From what you've posted, your daughter CHANGES hairstyles a lot! She's trying to find herself, and hairstyles are the 1st to show INDIVIDUALITY, being themselves, and in your case, she's getting some pressures from HER friends. (I started showing 'myself' when I started styling my hair by 1st grade. Many girls today, don't have a clue what to do with their hair, until they're 35 or even older, and just allow the salon takes care of their hair - because they don't know how to do their hair). I've seen women in their 80's, STILL trying to find the best style for their hair, and does what your daughter do!
With that said, no matter what she does to her hair, IT IS HER hair. I've been a teenager, and my mom hated my long hair, but she cuts them off where I wanted it. She didn't give me a smile of approval, until in my 50's, when she heard someone complimenting me with my hair, and I can do various hairstyles per week.
The only times I will probably get upset, if she started changing her hair by using too much chemicals, after I give her sources, about cancer. In my family, we have a DNA of cancer, and hair dyes just add more risks. AND/or using heat to style her hair, which stunts the growth of her hair, and the reason why many girls/guys have hair falls. Other than haircut, I have no problem with length or shaving, HAIR will grow back.
This is part of GROWING UP, so let her! If she gets denied because of her hairstyle, it''s part of lesson growing up. She'll LEARN!
A mother of 2 sons, who started styling & cutting their own hair from middle school - HS, even now in their 30's & 40's, and grandma of 2.