Sounds like you have reached the end of your tether op. Fair enough, I have been through "interesting" times with teens and am only just coming out the other side. I know it can be seriously hard.
But come on op, you have written six lines about your DD and we are supposed to have an opinion on whether she should go to boarding school or not? Were you venting (if so fair enough) or are you serious?
As others have said, no, generally speaking, boarding school is the last place you should send your child unless you are extremely depressed or you are moving around for your job or there is some other significant reason why.
Your dd is separating herself off from you in order to become a separate individual. It's a bewildering process for her and for you. She is going to challenge authority, assert her new found "power", test boundaries, reflect back your limitations as a parent (which we all have) and frankly a lot of it is a pita. But it's our job to be there, put up with a lot of the crap, set boundaries for the rest, act as a shock absorber for some of the emotional fall out, model the behaviours you want her to copy, and try and help her with her emotional regulation band decision making skills. Try and keep the lines of communication open and adjust your parenting so it's not "you do this because I say so" but "you do this because a b and c and yes I admit I find it hard too but I am doing my best and I expect you to try and do your best too".
Good luck op. Just being there alongside them and holding the line is half the battle.
Get some support for yourself and read "Untangled" by Lisa Damour.