I know how you feel, my dd1 who is also 11 was behaving exactly the same, it was really getting me down tbh, I was getting a lot of headaches and felt a weight was on my shoulders, it was really hard work and tiring.
Christmas eve she came down with the cold/ flu illness everyone has had. Christmas day she sat opening presents with a couldn't care less expression which was heartbreaking tbh, the only ethusiasm she showed was when we opened our presents which was nice but I was still heartbroken she didn't seem happy about things we'd carefully chosen and struggled to pay for. DD1 said it was because she didn't feel well and that's why she lacked ethusiasm. She then spent about a week lying around watching tv, pretending to sleep and ignoring us, I left her to it because I thought even though she was laying the illness on thick maybe she needed the rest after all she had had a long term and started a new school but I was worried because she said she had lost her appetite and was barely eating, in the end I settled for the fact she would drink milk, I was on the verge of taking her to the doctors about her weight as she is very tiny for her age but the more fuss I create the more she does it so I just made sure I brought things I know she usually can't resist and it seemed to improve her eating a little bit but not that much.
Dd1 then went to her grandparents with her sister and cousins and they went out for macdonalds, dd1 ate it all and had pudding (which she hadn't done for over a week) partly because she was feeling better by then but also because her grandparents wouldn't have put up with her messing about and also because the other 3 children are really good eaters I think so she came home a lot happier and eating a lot better.
Something seemed to click she started behaving a bit better, whether it was the rest she'd had or the fact she had seen how calm our home was when she had been lying around and not causing tension I don't really know but she has been so much better behaved, like a different child, it's been amazing! All of a sudden she's done things like thanked me for making her lunch to take to school, gave me cuddles and kisses a lot more, txt me from school saying hi mum miss you love you - so I said to her carry on like this and I will allow you privilidges like watching tv in your room for a bit in the evenings, take her swimming when her sister is in bed, watch a film with her, take her tobogganing she was so so happy with these ideas and was so grateful, I was suprised by her gratitude because its not like I haven't tried to reward her for good behaviour before, it's just normally she can't keep it up long enough to get the rewards!
I told everyone who would listen how proud I was of dd1, all the good things she had been doing, basically everything I ever ried to teach her had sunk in and she was behaving so brilliantly, she was a pleasure to spend time with, I explained how much weight have been lifted and how much happier I felt and how the atmosphere in the house was so much nicer all because she had changed her attitude towards us, I wasn't constantly telling her to mind how she spoke to me or her sister, I wasn't reminding her about how to behave, nagging to do as she's told etc for nearly 2 weeks she has been wonderful and lovely and she's been so much happier too.
Then yesterday morning she lost something, we all helped her look and in the end I gave her one of mine and promised to replace hers at the weekend she mouthed off at all of us then sulked and ignored us she went off to school and we were all upset and cross we feared she had been faking her new improved behaviour and had known all the time how we expected her to behave but just couldn't be bothered because she didn't care or respect us enough. I tried to remain positive, it was just a blip, we all have off days, she was upset she'd lost something and had taken it out of those closest etc when she came home from school she apologised and then was brilliantly behaved for the rest of the day.
My hope was restored but shaken.
This morning she was behind me drying her hair i said jokingly oh ur blowing my hair too and she snapped at me and though it was just one line, her tone and the way she looked at me really upset me and it was as if I had dreamt the past 2 weeks. I felt stupid and naieve to have believed she could have changed that much so suddenly. But then she apologised and cuddled me and has since text me and seems to be trying to make amends SO I am going to give her the benefit of the doubt BUT I am going to expect the new improved behaviour not only because I can't take any more of living with the old behaviour but also because she has now proved to us that she can be well behaved and lovely and I am not going to let her get lost and go back to making us all miserable.
Good Luck and I hope for some good luck too. It's a hard thankless job at times isn't it but there isn't really any options but to carry on and keep fighting is there?