We have a blended family his son (12), my daughter
(12) and our son (6). I cringed when my step-son came to our house. He has done numerous things to make our house a living h**l. He has carved his name into my dining room table, sat at the table and refused to eat diner, wouldn't take his coat or shoes off for hours after arriving at our house, purposely stuck his finger down his throat and made himself vomit only to stand there and laugh while I cleaned it up, tried to strangle my sisters dog with his leash and collar, urinated in his closet, ignored me for entire weekends when he was at our house, AND LIED LIKE A DOG!
Now I'm not saying that I'm a perfect mom; I do however expect all of the children in my house to live by the same rules when they are in my home. Not to mention that we home-school so everyone in our house is pretty set in their ways and there's not usually any sibling rivalry. It finally got to a point where he disrupted our house so much when he was here that we couldn't enjoy our time with the other kids. My daughter and him were on the same visitation schedule so if I didn't get to spend time with her on that weekend I wouldn't have her the next weekend, or any quiet time for my husband and me. We just finally had to remove ourselves from the situation when the mother wouldn't back my husband up and endorsed his behavior. The mother didn't see that there was a problem and refused to help or to get him help. Don't get me wrong, there is an empty place in our home and hearts because we had to make this decision. We had to do it for our other kids because their safety was starting to become a concern.
I think you need to figure out if your feelings about your SD are truly because of her as a person, or maybe some underlying issue that about her mother. I know it's hard to see a "clone", and 12 year old girls are really hard to deal with. TRUST ME! My sweet, passive, enthusiastic, out-going, giving daughter has turned into a monster with 3 heads. Some days I just wonder if I tried to knock two of them off if it would be child abuse.

I think at this age they have a great understanding of their home lives but deeply question their own place in life and are trying to figure out who they are. It's also a time where we need to re-evaluate the structure of raising them. They aren't babies anymore, they aren't grown-ups (even if they are almost as tall as we are), they are still these 3 headed creatures that need rules, compassion, understanding, open communication, a firm hand, and a loving heart to share the scary things that are going on in their lives. Maybe all the drama is covering up for some deeper underlying conflict that she has in herself or with someone else, a defensive-survival method.