I feel for you! As a mother of 4 girls (ages 30 - 17) I've been there & done that. Really -- you'll both get through it. You sound like you're trying to gently guide ("gently" being key here -- good for you!). Isn't it awful how sometimes this is easier said than done?
I'd agree with letting someone else do the shopping with you. I've used an older cousin with my daughter -- and my 18-yo has gone with her best friend & her friend's mom for years as an intermediary.
As a twist, though, if you can't think of anyone, go by yourself to a store you think she'll like. Look around & see what you think about their clothes. Find a smart salesperson, explain the situation & enlist her help. Go back w/your daughter & let the salesperson do her job. You, of course, have the final say -- gently, of course.
Good luck! A thick skin and patience helps...