Whilst I've taken children home for less... I'd not write this little girl off just yet.
Two of my DS (12)'s friends were both actually banned from my house for appalling behaviour/attitude - one when my son was 6, and one when my son was 9.
The first boy was banned when he repeatedly ignored my telling him not to jump on our (brand new) sofa and certainly not with muddy shoes on. The second time he did it, I told him that if he disobeyed me again, I would take him home and that would be the end of his coming into our home. He looked me dead in the eye, grinned... and jumped on the sofa whilst shouting "fuck you!". I marched him home. Told his mother what he'd done... and got "oh, X would never do or say that!" in response. Well, lady, he did and he has, and he's banned!
The second, was because of the arrogant way in which he totally demoralised my son, belittled my daughter, and sneered at me for working from home. Again, taken home. My son went to his house a week later for a few hours after school (came out of the school gates, "oh, please can I go, Mum, pleasepleaseplease?!" sort of thing) with no black eyes/lumps on his head. I collected him from their house... black eye and a massive lump on his head. The mother? Had no idea what on earth had happened... it wasn't either one of her beloved boys... he must have done it at school! Turned out that the older boy had shoved him over so that the younger one could poke him in the eye with a light saber. Banned. If I could have proven it... the police would have been called, but my son was ridiculously upset about it and just wanted to forget about it.
Today? He's friends with both of the boys who are banned from my house. They walk to senior school together, they play in the local park together, they ride their bikes together. The two boys also know that I don't stand for any nonsense, and that when I say I'm going to enforce a consequence for the choice they've made? It stands. They arrive when their parents aren't at home, forlorn looks on their faces, and know that I'll make sure they're okay. Also that I can contact their mothers on social media and they'll respond to those messages whilst ignoring their son's calls to their cell'phones...
Today, the boys are all 11 and 12. They're polite, they're respectful and we have conversations about history and why I make my son wear a helmet when he rides his bike (actually, I don't: he chooses to because he's seen the long-lasting damage of a brain injury within the family). The first boy, the "fuck you!" sofa jumper's mother woke up to his behaviour and dealt with it. The second boy's mother is still oblivious to it all - his younger brother's one to avoid at all costs, still, I'm afraid! - and likes to blame their friends for it all. Some parents are like that, though. At the moment, her older son respects the rules for/in my home, and that's all I can hope for.
So give Little Miss PITA a very wide berth with regards to her setting foot in your home, but don't interfere with your daughter's friendship with her. She may be like the two boys above and grow up/realise that she's missing out because of her behaviour/change. In a few years, your daughter may have made the choice not to be friends with her anymore, and all's well that ends well. But that has to be her choice, I'm afraid.
It is, however, your choice as to whether she ever sets foot inside your home again.