Is that all the help you've been given, no coping strategies or ways to simmer her down? Who has given this advice by the way, exactly what direction have you been pointed in for help?
My 9 nine year old DD can also also be very headstrong, stroppy but rather than tantrums she wears me out with debates/questions/arguments about EVERYTHING, she is quite jealous of her older brother at times. Do you see yourself any reason for her to be jealous of the 7 year old, does she feel perhaps she gets a lot more attention as she's younger, would you agree with the 'advice' that this is the main cause of her tantrums?
I can't imagine that your daughter likes the situation any more than you do that you don't go out because of her tantrums. Have you calmly spoken to her about what's going on, about the fact that her behaviour is not on and that it prevents you from doing all the things you could be doing. What is she like with other people, what happens if anyone else takes her out?
Have you let her get away with 'smaller' strops and sulk and cheeky tones that you shouldn't really have tolerated? I know me and DH have done this with our DD and just last week said to her that as soon as she uses her cheeky/cross tone of voice that she often uses she will be doing 'time out' on the stairs (I know it's a bit Supernanny but it's a good a place as any!) and I also told her she is getting to old to be doing 'the stairs' to make her stop and think. All (?) children like to think of themselves as acting more grown up so I am trying to shame her into not acting babyish.
You can't carry on like this as it's obviously preventing you from a normal life, please seek more help from a professional source if needed, don't be fobbed off with the stuff you've already been told. Even if this is the answer to her behaviour you obviously need help with her not just to be told to put up with it! Hope this helps a little and she calms down soon ( along with my DD, perhaps we should put them together in a room and they can wear each other out).