I suggest that you read the book, How to Talk so Kids Will Listen and Listen so Kids Will Talk by Adelle Faber and Elaine Mazlish. How we word things makes a big difference in how other people hear them. I think you may be right that she is rebelling. I suggest you can change how she feels by changing how you talk and perhaps more importantly how you listen to her.
We usually start nudging our child into saying thank you while they're still a toddler. Sounds like that didn't happen with her. It's not too late to nudge her now. I suggest that saying thank you is a learned social skill and should not be taught thru punishment which is what taking away is. Taking something away creates anger instead of a sense of thankfulness which you're trying to teach her.
I adopted my foster daughter who came to live with me when she was barely 7. Her caseworker told me that I needed to begin with her at what age in maturity she was. In many ways she was still a preschooler. She was taught manners. But missed out on learning a sense of security. She played the game that toddlers love of hiding and wanting me to find her. She scared me at times by doing this outside or at a store. When I told her I was frightened she didn't seem to understand. I didn't understand why she was doing this and her counselor said I should refuse to play the game. I tried but was unhappy doing so. My foster daughter continued to hide and I continued to look for her in a grumpy way.
Now I have grandchildren and my granddaughter started this game when she was 3 or 4. She was giggling while doing it and it was always easy to find her. I felt relaxed and enjoyed the game. She's now 10 and still plays "where's Monet." She makes it easy for me to find her. The mood of the game with my granddaughter is altogether different than it was with my daughter.
If I'd had experience with this behavior before having my 7yo foster daughter play it, I would have handled it altogether differently. I would laugh and search and in good humor say that she's so important to me that I get scared sometimes and then worked out some boundaries for playing the game. As it was, the game was more of a power struggle than a game. Because I didn't know better, I remained serious and focused on ending the game instead of having fun and controlling the game.
I suggest you back off and start over. First talk with her and tell her you made a mistake when you decided to take things away. Then ask her how she feels about your taking things away as well as how she feels about saying thank you and why she won't do it.
I suggest that you're in a power struggle with your daughter. First, being self-centered at this age is normal. We only learn compassion for others as we emotionally mature. It sounds like your daughter is stuck emotionally and/or socially at a younger age. I don't know how old she was when she came into your life. If her early life was unpleasant and her mother didn't teach her the things you're working on now then think back to the age at which she would have ordinarily learned it and start from there. Talk with her as you would a 9 yo but only expect from her what she should have learned but didn't when she was 4 or 5. This will help you feel less frustrated and be more relaxed and playful while you teach er.
When you tell her that you believe she doesn't appreciate what you're doing for her, you're also in a minor way focused on yourself instead of on her. This is a small piece of being self-centered. Don't get me wrong. I've often felt that way and expressed that feeling to those in my family. It never changed anything.
I suggest you focus on her and how she feels as a way of modeling compassion. Yes, you can mention that you feel unappreciated but the focus needs to be on her and why she is acting this way. Remember, she is a scared little girl who has some strong feelings with which she needs help in learning how to deal with them. She has learned to manage by being defiant or passive. Those ways worked for her when she started using them. Now, you're needing to teach her and she'll learn best if you can accept her the way she is and show her compassion for having to learn them now. The book by Faber and Mazlish will help you in how to do this.
All children need to be filled up with love and a sense of self-worth before they can be concerned about anyone else. I suggest that you practice praising her often. Set up a reward system. Perhaps a sticker chart on which she gets stickers for completing chores. Be sure she spends special time with you and her father every week no matter how she's behaved. Actually, spend at least 15-20 minutes with her, doing something fun, every night. Make this a time focused on fun and not on discipline or doing things "right." Show her in words and actions that she is a special little girl and that you love her no matter how she acts.
Be sure to talk with your daughter in a calm and kind way even when asking her to do or not do something. You can be firm and kind at the same time. I'm glad that you're working on one thing at a time. I suggest that you start over with the thank you lesson. Talk with her about it. Understand and accept her feelings on it. Perhaps ask her what you can do to help her be polite. After a period of time doing nothing you could try nudging her lovingly to remind her. Tell her you accept some responsibility for her having not learned to say it. Do not react if she doesn't say thank you. Don't mention that she didn't. Praise her when you're alone for saying thank you when she does say it.
My grandson was angry when it was bedtime and said he wasn't going to put on his pj's. At first I was firm and insisted which only increased his rebellion. When I realized that this was escalating into a power struggle I said I was going to brush my teeth and hoped that he would have his pjs on when I got back. When I got back he said he was sorry and the something that sounded like, "you started it." He has difficulty with speech and so I asked what he'd said. He stuttered around a bit and then said, "we in this together?" I chuckled because I was feeling we were definitely in this together and I didn't know, yet, what my next move would be. I then said that yes, we are in this together. He smiled big, said a definite "sorry" and gave me a hug. Everything went smoothly after that.
When I'm tired, especially, I find that I become firm and inflexible as I say, you do this, now. I can even feel myself as being outside the relationship, focusing on making something happen without regard to the child's state of mind. I'm the grown up. You're the kid. Do as I say. in a somewhat cold voice. I just wanted him to get in bed so I could go to sleep. When he's tired, that does not work. I'm so proud of him for being able to bring me back into the relationship while doing what I'd told him to do.
After that I read him a story. Perhaps if I'd read him the story before I told him to put on his pjs or if I'd asked him instead of telling him, I would have had more success. I just try different things and sometimes they work and sometimes not. This incident was a big "a ha" experience for me.
When a toddler, preschooler first starts to say thank you, it's rote. With time they learn to mean it. Your daughter is just learning. Rote first. Meaning next.
Also, remember she is a child of divorce. She has a whole lot of anger built up inside her. Counseling would help all of you in learning how to relate with each other in this environment that is certainly much different than the one she had up until now.
I would like to add that perhaps you need to spend more time developing a relationship with her that is based on trust before you try tackling the more superficial aspects of life such as manners. I don't know how long she's lived with you or even if she does live with you. That will make a difference. I've been thinking she lives with you. If she doesn't some of my answers would be different.
Are the two of you able to cuddle together, sing songs, read stories, and in general have fun? Developing that kind of relationship takes time and is of the highest priority. My foster daughter wouldn't let me hug her or be physically close to her until she was an adult. That was difficult. But we did learn how to have fun. I always read to her and we had some serious conversations at bed time and while in the car. She did not respond well to a serious conversation at any other time.
Perhaps taking a parenting class for foster parents might help you if your daughter is as much different from the average child as it sounds.
While a foster parent I took a workshop from Foster Cline. He and a colleague wrote several books. I think the first one is Parenting with Love and Logic. I highly recommend reading it. Children with a rough beginning for whatever reason do have a different outlook on life and may need different sorts of parenting than a child who began life in a warm, loving and secure home. These skills also work very well with typical children.
