It sounds like that if there are no know health issues involved that you are working in the right direction already. Consistency is the key, which you already said they have been very consistent. The tantrums and whining getting worse my actually be a good thing. It may be her realizing that she can no longer control others with her attitude and is in distress because of it. Don't give up or give in. Continue to be consistent and I think she will come through. I know it is tough, but she will thank you for it when she is older. I have many times been thankful for all the time my parents punished me when I was a child. I would not be the person I am today if they had not punished me for wrong doing. Keep it up!!!!
I hate to even suggest this, but it may be more that just a learned behavioral problem. I have a son with diagnosed severe ADHD and you just described him prior to ADHD meds. In fact, he is 10 now and I decided to try to take him off his meds for the summer. It lasted less than a month. He became aggressive with his 5 year old brother and 3 year old sister and I was afraid he would hurt them. I put him back on meds this week and the difference was visible immediately.
Also, my 3 year old has been anemic several times since birth. I know when she is based on her behavior. She gets fussy, cries at the drop of a hat and wants things her way. The doctor will test her blood and inform me that she is and prescribe a iron supplement and in about a week her attitude improves.