Hi there out of ideas. You've tacked your post onto an older post and those often get missed. For more responses, it helps to start your own thread which you can do by going to the top of this page and hitting Ask a Question.
I just wanted to comment that I too have an 11 year old. Some of what you are seeing is the age. Not so much the lying part but the lack of motivation for chores and such. My son has found his inner self which I guess likes to hang out in his room a lot. :>(( Hard sometimes to get him to do what I'd like for him to do when he used to be a bit more cooperative.
the issue between you and your partner is challenging. If you two aren't on the same page, it makes it very stressful to deal with kid problems. Can you talk to him about that (in a way that doesn't make him defensive about his daughter?)?
I'm having the exact same issue with my stepdaughter. She is also 11 and I have also had her since she was 4, her mother is drug addict and rarely ever sees her, she has lived with us full time since I met her dad. She lies about trival things that don't matter that I know 100% she is lying about and her dad backs her every single time. These are things that wouldn't matter... Like did you eat all the cookies? No. When she was the only one home. She is also extremely lazy, she will pretend to do her chores and when I question her she will say she forgot or she did do them just not as good as I would... It's to the point where her father and I argue about her all the time, he will call me a liar and a bully and say I'm attacking a child, when in reality she has the wool pulled over his eyes so tight. She like your daughter is loving and affectionate to me and calls me mom but she is constantly lying about stuff that doesn't matter... Please help, tell me something that you tried worked. My next step is divorce because I can't take it anymore.
I think she sounds like she may be depressed - isolating herself and talking to stuffed animals sounds like she is just "checking out". I was exactly like her when I was young and my mother died at the age of 3. One year later I was sent away from my father who I loved more than anything to live with relatives. I was heartbroken and devastated. I never got any counseling - people just assume kids are resilient - and that they are so young they won't remember - but they feel things more than people know and do not know what to do with all these incredibly strong emotions. So they act out in sometimes strange ways. She may have a lot of emotions/negative thoughts that have to do with her mom leaving her. I know it was a long time ago - and she has you now - but it doesn't stop kids from thinking "what is wrong me that my mom left me?" That alone can be devastating to some kids. In my case I had no ambition, no zest for life, I was lazy and wanted to be alone. I, too, would spend hours and hours in my room by myself. I just felt no connection to anyone because I was afraid to be connected and get hurt. I really wish someone would of taken me to counseling at that age. It might have saved me a lot of grief trying to undo the depression/anxiety I've lived with all my life. Instead all I got was a lot of people calling me lazy, sloppy and weird. In my opinion the best thing you can do is take her to a good counselor and also as the above post said - try to get her to join something that she is good at. Good luck. I'll be thinking about you both. I hope she gets some help so she (and you) have a more joyful life.
I would take her back to see another psychologist or a psychiatrist and have them nail down some sort of diagnosis. If a therapist isn't able to give you and your daughter some advice or answers that help your situation then try a new therapist. It doesn't mean they are incompetent, but you need to find the right fit for you and your daughter and that can often take several tries. Did you get any help or direction from the psychologist you did see? Did they offer suggestions on how to handle her behavior? She sounds a bit passive/aggressive, but I'm certainly no expert. I would definitely pursue therapy. Also, don't blame yourself, you care and you are doing the best you can. You may find there are ways you can help her that you didn't know about, you just need to find the right help. Good luck, be persistent and hang in there!
What does she do passably well? Soccer? Swimming? Helping out at the Animal Shelter?
She needs to find an identity, and friends who appreciate a skill she has. Is she going into middle school next year - can she play an instrument in the band?