Well, probably, nine-year-old sister is more mature and responsible because she isn't a young teen yet. Sorry, but that may be the case.
I don't think you hate your older daughter. You're confused, frustrated, and a little desperate. I think you don't LIKE her very much right now. She probably doesn't like you a whole lot either. That goes with the young teen territory.
What are the consequences for her substandard behavior at home? If the main consequence is listening to a lecture from Mama, you need to get a better one than that, because it's not working! It sounds as if she's using passive-aggressive tactics on you - being "nice" and agreeable, but steadfastly refusing to do what you ask. Call her on that. When it comes to having a good effect, meaningful consequences beat nagging every day.
If it were me, I'd call the therapist back and say, "I've changed my question. I don't want to know how to change my daughter. I want to know how to change myself." You want to talk to the therapist about the fact that you want to quit the nagging forever and need to know what to do instead.
Pretend that you like your daughter. Really. Pretending can sometimes help. Smile and say, "Good morning," to her when she gets up, no matter what her response is. Be sure you say "I love you" (not "I love you BUT") to her at least twice a day, no matter how she behaves and no matter how you feel.
Did I ever feel that way about my children? You bet. But we survived. You will, too.