Here is some advice that I am very confident of:
1) Do read the "How to talk so your kids will listen and listen so your kids will talk". I would start with the original one, which lays down the basics and teaches the basic skills. I have not read the ones specific to teens, sibling rivalry, etc., but it seems to me that the original one is so solid that there is no need. I read this book in detail, as a textbook, cover to cover, three times, over a period of ~10 years. I needed to learn parenting skills (also had an abusive mother, though not as bad as yours), and this book, as well as some other material on positive parenting (e.g., the word "discipline" has a root in 'teaching', so you should understand yourself as a teacher, not police), helped tremendously. Each time I read the book, some additional skills would stick. It's a process. You can only learn so much at a time.
2) Related: In my experience, punishment works for "regular strength" misbehavior. If you have rapport, it will correct behavior. If you have a good relationship, it will correct attitude. If things are out of control, which they seem to be, it will not be the answer. If you double-down on punishment, your daughter will double-down on rebellion. In my experience (with an impossible, physically violent 4 year old), the less I disciplined, the better he behaved, though it was admittedly hard to get into that virtuous cycle. It seems that with the relationship you have with your daughter now, the best you can hope to achieve with punishment is to have her stop the behavior _while you are around_, and that only if you find something painful enough to punish with. The pain will surely inflict damage, so you have to weigh priorities, such as your sanity and little brother's emotional well-being vs her emotional well-being. That's a no-win.
3) After you described your childhood, I am pretty confident that therein lies part of the problem. Therapy is great to process your trauma, but doesn't teach parenting skills. You may 'know' that something is wrong, but that's completely different from being able to do something different or knowing how. Instead of negative knowledge (this should not be done), you need positive knowledge (that should be done). Study up on parenting skills, best from books, and practice, practice. Good behavior will not feel natural for you.
Now some advice that could apply:
4) It is very possible that your husband is a large part of the problem. If he yells at your daughter too much (which is abuse, btw), she is likely angry at him for that, and at you for allowing that to go on. How to fix that if he is the primary caregiver, I don't know. My daughter was not that angry, and has a more compliant personality, and wasn't particularly angry with me, and an honest talk helped some (I think). I explained that no, dad's behavior is not normal, he has problems with his anger, there is something called 'intermittent explosive disorder' (which I think is just a fancy name for 'aggressive self-centered jerk', but it helps to not make things personal), and that dad needs anger management therapy, which I suggested to him and was laughed off. Daughter was 11, and would be clearly distressed by his out-of-control yelling, and I just figured that she was too old to keep that papered over. She still gets very angry at his outbursts, (even when she is in the wrong, heh), but at least she has an outlet, she can complain to me, and I hope having a pressure-release valve will help in the future. So, no defiant behavior with me. There is very little, but slowly growing, with dad.
5) Without too much sugarcoating... Your abusive childhood sets you up for being abusive. So you need to learn positive parenting skills on your own and purposefully. See 1) and 3). Also, it sets you up for marrying someone abusive - not necessarily because that's what you feel comfortable with, but because you are the person that does not see 'red flags' that other women see. So, you end up with an abuser because other women picked milder-mannered men. Also, women who stand up for themselves are not attractive to such men for long. If this is your story, you're in a pickle. You need to protect daughter from abuse, or at least give appearance that you're trying, if this is to get better. This is not going to work until your parenting is not abusive, and even then, it's going to be hard. So, a long road ahead of you... Part of how to keep sane is to recognize that this is a difficult situation that may not have good outcomes, only more or less bad ones, and your job is to minimize damage. You can't change the past, but you can work on making the future as good as possible given the circumstances.
Again, something I am very confident of: you don't put out fire with gasoline, so you don't put out anger with punishment.
