My third, also a girl, is this way, in a BIG way. She' only two, but started the difficult behavior at 9 months (my older two never did anything defiant or angry before 18 months!) and has taken much more discipline. She is leaps and bounds ahead of where she was, now she's better than most typical two year olds, but for the amount of discipline it has been, I'm amazed how difficult she still is.
All I can say is, SOME kids are like this. You're doing great. The discipline you have been using has helped immensely and she would be off the charts terrible if you had not been firm. You'd be suspecting her of disorders by now. I come from a massive family, and some of the kids were this difficult. They all turned out great and happy by about 5 years old. Being firm for wrong behavior does not squash strength of character, it channels it. They still have extra spark and spirit in spades, but are very good.
My daughter has control of her impulses, she just has a lot more scary impulses and a huge temper! Sometimes when we hit a rough patch, I really firm up on the discipline, like give less warnings before acting when she tries tantrums. She never carries one out, because shes not allowed, but she still needs warnings and occasional discipline if she's let out the warning shriek a few too many times in a day. We had to outlaw and discipline "no" with her, because she used it as an intro to a melt down and constant defiance, so now she knows not to say it. Even if she does say, "no" she immediately knows she's on thin ice, you can see it click in her own mind as soon as she says it, and she won't launch into a fit from there.
I also really step up the positive attention and nurturing during these phases, because she is worse if she's bored and frustrated.. Giving lots of choices is fine, but avoid it as a way to avoid the confrontation when discipline is needed. Never back down, remain calm, and she will continue to learn. As much as I sometimes feel it's and endless battle, I am amazed how good she is now and lots of people compliment her knowing how difficult she has always been. When you stand back, it's just the typical spirited way, nothing more. I look forward to her strength going forward in life :)
This book has been great with all of my kids, even her Back to Basics Discipline by Janet Campbell Matson. It was really rewarding recently to spend time with a friend exactly my daughter's age, only with a much nicer nature, for a few days. Her daughter is a typical undisciplined two, only gets time outs and uses them to tantrum, and my daughter behaves way better! She minds what I say, and at least she'll control a fit rather than launching into it, even though she still gets mad. My friend's daughter just goes with each fit as it comes along all day, so she's CONSTANTLY crying, whereas mine isn't. It hasn't been easy, but it's worth it to keep at it.
Good luck!