I am so sorry that you have to go through this! I went through the same thing last year with my DD. (same age as yours) Well as much as it broke my heart and trust me it really broke my heart I let her go.
Well, within 4 months she was calling me and begging me to move back home. I made her stick it out two more months (6mo total) and then I let her come back. She is like a totally different child now. More manners and less attitude.
I forgot to mention that her dad lives 18hrs from here.
So, as much as you don't want her to go its best (not easiest) to let her do it. She will then see that you are not as bad as she thinks and that they are not as great as she thinks.
Once again I am so sorry that you have to go through this!!!