What you can do is realize your child is a child and she isn't going to be handling such a changing landscape of her life as easily as you may assume a child would. You said her birth father was an alcoholic, and this has the potential to be traumatizing to a child even if no abuse occurred. You made the amazing and difficult decision to make him leave, of which you should be proud of, but to a child it's a difficult thing to process.

This girl isn't intentionally going out of her way to drive you mad. Despite what people think, children really don't have the ability to know just what ticks someone off until they are in their early/later teens (when teens say things they know get at their parents like "You're a terrible mom!" because they understand the initial reaction from the parent). She may just be having a hard time handling this situation internally, even if it happened in a span of years.

I think a good course of action is finding a therapist or counselor for children so she can learn to work out stress and anxiety (which could easily be causing aggression, fight or flight), internally and so you can also have an open dialogue.