If you're open to her about it and go with her, it's not about only her - framing it in a way where it's about working on your relationship to her might help.
Like I said children can take some time to come to terms with things one day it's all peachy and wham. At the same time she's 8 it's possible as well that her hormones are starting to change (that does happen at her age in some girls) and she's not able to deal with them.
Her pulling her hair out and hitting herself is not good. I would still try and talk to her openly, and if she does say anything really listen to what she says, too often parents don't because she is "just a child" but she needs to feel heard and respected too.
You said the problems started about 3-4 months ago and the baby is now about 2 months old, it may not be the case but I'd say there is a strong correlation there - babies take up WAAAAAAY more time of parents than do children (like her sister and step siblings) that's a big change to adjust too with everything else she has already had to adjust too. That's asking a lot of her even if it's over the span of 2 plus years.
Seek help - don't frame it in a negative light and she will be ok. Even if you go first by yourself to get a feel for the pyschologist - as you said if she is having trouble managing her anger then that has to be addressed because it will only get worse as she gets bigger, stronger, more independent. The fact that she recognizes her wrongs and apologizes later is definately a good thing but really she need not be getting that upset to begin with (at least not as frequently as you say). IT's ok to be mad and upset, but it is not ok to say hurtful things and hurt herself or someone else. Keep talking to her, every day and I would seek professional advice, even if you don't take her directly although I think if you did it would only benefit her.
Thanks for your response. Well the new baby is a couple months old only. Born late September. My daughter does have a younger sister who is 6 that lives with us as well. Also she has 2 step brothers that live with her dad and step mom. I do have 2 step sons as well but she doesn't see them as often as her dad's step children. It has been this way for 2 years now. It is not until recently I started noticing the change in her behaviour. Like I mentioned before, it is just a little strange that she has never been the type to talk back or raise her voice to me or be self destructive. Just recently it began. She has even on occasion said that I am the worst mother (when I discipline her for her wrong doings), and she has said she hates her life. I always tell her that she has a great life compared to some children out there. She is very fortunate to have so many people in her life that love her. Then when she cools down she will write me a sorry note and tell me not to listen to her when she gets angry and says ugly things. I don't know what the cause is but I am scared to seek help with her because I feel as though she may think she is a bad child or something. She is a sensative person.
How old is your husbands new baby?
I'm guessing the entirety and finality of the divorce is hitting her with the birth of the baby and at 8 she is much better able to understand what divorce is and it's consequences - even if it's in the past and you both have remarried having a new brother and sister but understanding that your mommy and his/hers is not the same is something to swollow I believe. That may or may not be the entire reason behind the behaviour but I bet it is at least a contributing factor. She now is competing for Dad's attenton and she may be letting it all out when she's at home with you, not with him.
I would keep trying to talk to her, and when you ask her why she acts that way don't leave the question so open - probe ie. ask her if she's upset by the new baby, if she feels sad or mad because of him/her? Ask if she's happy at school? Do you see what I mean? You need to leave it open for her to answer herself but directed enough so that you will actually get an answer.
She may very well benefit from some counselling to help her deal with her emotions and cope with the divorce - often children from divorced homes don't express the effects of the divorce until years later. Even if you and your ex have a good relationship when it comes to parenting - this is a change she may just not be able to handle.