Church camp with defiant teen

Miss 13 has been horrid on and off for a solid month – we are currently at the scheduled annual family church camp where she has activities morning evening and night – she’s hateful through the day when we see her –
I was hoping we would be getting better connection but she’s just been escaping to her friends – In the morning today she woke up late and she ran off saying "I hate you get away when I attempted to greet her – so i followed her to her activity & required her to give me a hug – I realise she was stressed & wanting to leave on time / but from the first moment in the morning she had been barking at me to help her get food and towels etc and I ought to have connected then…I felt somewhat satisfied letting her go on an “educational” trip to the island with the youth – I had required her to hug me for 30 seconds &token reinstated my authority by saying she was going as it was educational. She came back and was happy and pleasant for 30 seconds at a time before going to her friends. She played with her friends all afternoon after the trip & when she came back from the night meetings she declared happily "I am going to the football tomorrow with Lacey!" she was really happy initially and I wish I had connected with her & hugged her – I feel I ought to have said "tell me about it! Sounds exciting, did you enjoy the game?" But instead I felt somehow obliged to give her an instant answer… “no your behaviour has been nasty & what you said this morning – she said “I will be bad now. I hate you I wish you were dead “ Then she walked off – I went through the rule of 3 a but she attempted to walk away by locking herself in the car / I said you are in 24 hour no privileges – she went to the shower block and I went to bed – it's 10:39pm. – I am praying & wondering / do I attempt to check in on her in front of friends? She seems to be content to openly verbally abuse me! It’s sad for others watching – I just went and spoke to her in her tent – she initially resisted and then spoke boldly –
“Other people like me & get along with me – so you must be the one with the problem & who would want to be around you if you chase them down with consequences for everything? would you want to say hello to someone who locked you in a shed & starved you over night (referring to previous parenting coach we had!)she said told her friends. We ended with her saying she will jump on the bus for her ice skating event & threatening suiside because of me. I left calmly. What now