How do I deal with my boyfriends rude teen-age daughter?

We have been dating for 1 1/2 years, his 15 year old daughter is admittedly spoiled, but her rudeness and disrespectful attitude towards me is unbearable. My Guy is very understanding and tries to 'deal' with her, but he doesn't see the sarcasm or rolling eyes. I can't stand to be around her. I have 2 teen boys and I will not tolerate disrespectfulness, they refuse to be around her. For Example: In the car with 5 of us conversing, she loudly demands to change the station then sings to us all eliminating all conversation. Even though it's my car, all requests are made to Dad because we don't speak, "Dad, turn it up"; "Dad turn it down, I'm on the phone", "I'm HOT, Open the window". Last night I invited her to a barbecue at my house, her response "I'M NOT GOING!" Apparently she later reconsidered the invitation and told her Dad she will come if she can bring a friend. Occionally she will sing just for me, selecting beautiful phrases such as "Kill the *****", or, "Just die, die, die". When Dad confronts her, she claims innocence. On our last visit (as described above) she even asked him "did I behave well". I don't know if I'm crazy or if she is a manipulative BRAT! My boyfriend is very sensitive and she is Daddys girl, he waits on her hand and foot and sees his sweet little innocent girl. She has openly declared (in my house, in front of my kids and guests), that I am a *****, that he and I should break up, and believes that she can dictate her Dad and my relationship. When I attempted to deal with her at the onset, it got physical and ugly, now I avoid her. Should I just let her have her way and end the relationship?