Oh I can write a book on this subject, firstly. She is 16, & they can be so selfish & stupid at that age, believe me, its not YOU, its her ! she will grow up, she will improve.
You did absolutely the right thing taking her phone off her, You are going out to work to pay for her privileges, & she is 16, she knows there are rules, & she isn't playing by them.
She will soon be miserable with her father, or if she is on her own all week cooking & wandering about an empty house., He can pay her phone bill, He can make her do her homework, He can call time on curfews, or not? He can go ballistic if she trashes the house when he is ou or skips school...
"You can lead a horse to water but not make it drink", I know its a cliché, but she has been shown the way to behave, & she has chosen not to. the Only important thing is for her to not do drugs, & to not get pregnant, there is a solution for EVERYTHING else. Yes there really is, she might leave school, she might end up working in a shop, it DOESN'T matter, she is young, & there are loads of apprenticeships, & other ways to get qualifications.
She is currently living with her father, it's better than running away ! she may get fed up of having to do her own laundry, clean up after their dinner etc...
It is sudden & hurting you, I know exacly how you feel...but don't back down, she will only do it again if you show weakness. Just tell her the door is open, you love her, but her behavior is not acceptable. Try & do some of the things YOU want to do instead of running around after her...you deserve it.
Some years after my daughter came home after running away with all sorts of other major problems, she asked me for something, & I said "no", she said jokingly, "oh you have broken my heart", I looked at her, & said gently, "everyone gets their turn"..... she looked into my eyes, she understood at that moment, how she had broken my heart years before...
She is fine now... but my God it hurt.