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 – and is impossibly unfriendly through the day when we see her –

On the first day – I said “if you don’t eat you can’t go on the afternoon activity” I saw her before leaving and she said “I didn’t eat all the sandwich but I we some cereal” she hadn’t touched the sandwich snd had left messy cereal everywhere – I pulled her off the bus as they were leaving to talk with her / I gave her a choice of consequences – loose spending money or loose the swim trip / she chose to loose the money. When she came back she intimated I was at fault that that she didn’t eat on the trip as she had no money….she’s been reluctantly hugging me and even came to the bookshop for 15 mins with me yesterday and I was hoping we were getting better connection but 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 walked to find her at the leaving station and required her to give me a hug – I realise she was stressed and wanting to leave – 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 satisfied letting her go on an “educational” trip to the island with the youth – I felt I had hugged her for 30 seconds &token reinstated my authority – she was going as it was educational. She came back and was happy and pleasant for 30 seconds at a time. She played with her friends all afternoon after the trip & when she came back from the night meetings she declared "I am going to the football tomorrow with Lacey!" I said “you have to talk to dad “- she was really happy initially and I wish I had connected with her – 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 answer… “no your behaviour has been nasty and what you said this morning – she said “I will be bad now. I hate you I wish you were dead “ Then she started walking 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 –