That sounds exhausting! I think she is just strong willed and intense. Some kids are. There is nothing you are doing wrong and there is nothing wrong with her. She just has a different personality from your other two. Sometimes I think it helps just to acknowledge that this is just where your kid is at right now and remind yourself that she is still fantastic and lovable and unique.
It sounds like you are handling it very well. I disagree completely with spanking and think that sets up a bad dynamic between parents and kids. It also doesn't do much to teach her not to use physical force to get what she wants. And you want a cooperative, peaceful family, not a family based on threats.
So, keep doing what you're doing. Ignore her when she is screaming for no reason (I realize much easier said than done). Sounds like you did a great job with the diaper situation. Stay calm, continue to do what you are doing and don't give in. Screaming is usually to get a reaction. The less reaction she gets, the less interesting it will be (and she WILL grow out of this). If she is hurting her siblings, intervene as quickly as possible and remove her swiftly. Say "I don't let anyone hurt you and I won't let you hurt anyone else." You could either put her in a time out for a set period of time (2-3 minutes) or tell her she needs to be away from the family until she has calmed down. Either way, you'll have to keep putting her back in the time out for a long time until she realizes you really mean it.
I think sometimes it helps to mirror kids' emotions back to them and give them an outlet for anger. If you see she is getting frustrated, say "ooh, I can see how mad that makes you. You are mad! Maybe you should hit this pillow or kick this step or scream in the basement." Let her express her emotions, but not hurt people.
Hang in there - it will get better and some of this fiestiness will be a great quality down the line.
B.
PS - if this continues or gets worse and you think it is more than just a personality issue, call your pediatrician and describe these symptoms. It could be totally normal or there could be something more going on. Good luck!