I completely disagree the party should be cancelled.
For a start, she's having friendship problems, so cancelling a party which might have been an opportunity to have a wider group of friends over, and meet up with the other parents and start building new friends is really a mistake.
Also it's next week, and she's distressed and screaming now, you need to get on top of the situation now. Cancelling next week is a desperate act and basically makes you look like you have no control (which is true to be honest, I have never had any of my children's friends cancel a party ever, I would be quite surprised if we got a cancellation for that reason).
You need to go at this from two angles- a) how can you get to the bottom of what is distressing her so much she is screaming and out of control (which may actually mean more positive attention, reading stories together at night, chatting through the friendship problems, short love-bombing where you actually reconnect with her and stop seeing her just as 'bad' and b) how you can sensibly discipline her right now for bad behaviour and regain control in your own home. For mine, taking away the tablet/computer/TV time altogether, until people speak in a calm way, do not hit others etc works well, but it depends what works for her. If she hits her sister, that's a day on the tablet lost. If she is rude, I'd give a warning, then another day lost.
It needs to be short-term so there are immediate consequences, not vague threats of a party cancellation, which if it were to occur, would be very unlikely to make her behave better, in fact, she will go hysterical at the thought of all the children at school making fun of her, and very unlikely to solve your long-term issues with her.
I don't agree what you threaten you have to do, that works with three year olds but 8 year olds are older and need different and perhaps more sensitive handling IMO.