Hi R.,
I'm sure your feelings are very hurt, and you are concerned for your stepdaughter as well. I must tell you I have two sons and they both have told me they hate me! But I knew at the time that they loved me and they have come back to me since. At the time I said something like, "Well, I'm sorry to hear that. I hope you don't mean it, but even if you do I want you to know that I still love you. I don't like when you talk to me like that, but I still love you."
Teen years are tough business and dealing with hormones, growth spurts, identity.......well, it is all big. I'm afraid your daughter may have a rougher time than the average girl considering some of her "baggage."
This is what I would suggest if you can afford it. Family counseling. This does not mean you are sucked into therapy for a year. Two or three sessions may do the trick, but I think it would be good for all of you. If not that, then find another adult ear for your daughter. Does she have an Aunt or grandparent she could confide in? In her heart she knows you love her and she loves you. I feel certain of that with what you have told us, but teens need other adults in their lives that they can turn to as well.
All that said. I know you feel crummy, but your daughter is having a natural guilt for loving you...she is feeling if she loves you that she is betraying her natural mother. Let her know it is okay for her to love you both, but acknowledge her feelings and assure her that you will still love her, even when you don't like some of things that come out of her mouth. Even if she misses her mom.