PS Just a thought is she copying any friends have they "smart Mouths' Children do like to copy especially if it seems cool or clever, how do her friends speak to their Moms , have you heard. perhaps time to listen to the girls and thier attitude.
You sound very loving and caring in your Post, I doubt if you will ever lose your Daughter,you are really trying, I wonder if you are trying too hard, kind of overkill, how about you take a step back and when she yells and misbehaves treat it with nonchalence, dont respond to her, sometimes parents and kids get into a war of who can win.Before she yells things like' No dont hurt me' walk away, what triggers the out bursts see if you can ignore her before they start.Standing her in a corner is okay ,its the time out system and I know that can work, make sure she stays there till she is quiet and says sorry,if she is mean to her friends dont have them to your house till she is nice ,less words and more consistancy is the key here.