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She is not in treatment, she has lived in our home since she was 3 months old but her mother who is an alcoholic and drug addict comes in and out of her life. Her adoption was final when she was five.
I guess our biggest problem is she has two other siblings, which we also have custody of and they get to see their father and in her eyes their mother more than she does. ( they all have different father's)
She is angry that her mother does not show up for important events when she says she will. Also she always asks to go places with her mother and her mother will tell her that we will not allow her to go. So she is angry at us because she thinks we in a way are keeping her from her mother.
Thank you for the additional information. Its no surprising that she is angry and, unfortunately, is acting out her angry with you. This kind of behavior is very difficult to manage so I understand your frustration. I'm sorry to say that its unlikely that his kind of behavior will end soon, but it can stop. Children who suffer unstable homes and abuse often have attachment issues which has a direct impact on how they interact and establish relationships with others, including you. Given their life experiences its hard for them to fully believe, and believe it consistently, that adults will love and take care of them regardless of who they are or how the behave because history as told them otherwise. In some ways, she is testing you commitment to her with the negative behavior. I also agree that other factors are contributing to this behavior as multiple causes are involved in any form of acting out. However, I feel the attachment issue is primary and will resolve much of her behavior.
I recommend she start therapy soon. She can address the anger, learn self-soothing, and have a place where she can talk about the complexity of having a variety of confusing feelings.
For you, I recommend you read about attachment issues. Everything you mentioned that you are currently doing are good and helpful toward resolving attachment issues. These kids need a lot of love but they also need structure and rules. As you mentioned, yelling and losing your cool is not helpful. This is particularly true for this child.
Remember that the key to any behavior change is consistency. Although it may feel like its not making a difference, its making changes but they can be slow. I would add mirroring techniques to what you are already doing which helps with attachment and self-soothing. In other words, be her mirror so she is aware of her behavior. For example, "I know you are very angry and sad. I can see it in your face and behavior but its not okay to (describe the poor behavior). You have two choices (offer choices)" You can say, we can talk about how you feel or you can go to your room and calm down then we can talk.
I hope this helps. I've included a link regarding attachment issues. http://www.psychnet-uk.com/dsm_iv/attachment_disorder.htm