First...although you are having a difficult time, don't put yourself down by assuming YOU are doing something wrong. You just haven't yet found what works for both of you. Someone else has done wrong by her and she is taking it out on you.
Two suggestions for handling her behavior...
1. I bought a book called "1,2,3 Magic". It has really helped me with my 3 yo. It basically teaches you strategies for counting to 3 and being consistent about it. I used to work for a children's behavioral health agency and their therapists used it with clients. They highly recommended it, and now I do, too.
2. Have you looked at the way your husband interacts with her to see if there is something in particular she responds well to? Maybe you could try those techniques?
I imagine your neice's behavior is due in large part to what she has been through. But I also think age 3 is a tough one. My little guy wants so much independence (he wants to bathe himself, operate the DVD, answer the phone and the door) and also wants to control things (he tries to make house rules, tells his little sister what to play with, makes demands of me). I accomodate his requests when it is appropriate. I explain rules as clearly as I can and give him reasons for the rules. I use our experiences to talk about expected behavior and inappropriate behavior. I praise him for positive actions and (try) to be consistent in following through with consequences. I explain my role as his mother is to love him, keep him safe and healthy, teach him how to do things, etc. He reacts more favorably when I use a calm voice; yelling usually escalates a situation. After we finish a consequence I give him a hug, tell him I love him, and if we haven't already done so we discuss the situation. For the most part these techniques work for us. And I know he really hears what I say because at later points in time he will retell the situation or our conversation.
I hope something here is useful to you. I wish you well with the adoption and resolving the behavior issues.