Google prohibition. What did that do? Stop alcohol from being made and sold? No, by restricting it they made it more desirable. People got filthy rich from making alcohol and selling it.
If you tell your daughter she can't be around this girl then all you will accomplish is that they'll be bff's on the sly.
So, what to do?
Girl is welcome IN YOUR home, girl can come over and hang out and spend hours and hours where you can supervise them. They don't go in the bedroom and shut the door, they don't even go in the bedroom if you find things for them to do in the family space. Like watching movies with tons of sleeping bags, blankets/quilts, and pillows on the floor so they can lay down, eat popcorn and snacks, and watch movies til morning light.
You have them help you make cookies, make a craft, etc...things you can get your girl to do. You show how nice and friendly you are to this friend and your child will only see what a cool mom you are to her friend. So next time friend says something against you your girl will have recent memories of how kind and sweet you are to her friend and how you include her in everything when she's over.
The ulterior motive to this is that you get to see this girl up close and personal for a great deal of time. This girl might actually learn from you about manners and she might even start to respect you.
On the other hand if she's rude and won't follow your directions in your home then you need to have a talk with your daughter where you ask her how she feels about what her friend said/did towards you. What does she want to do about it because it can't happen again, etc...let your girl decide what happens.
But don't let her go to her friends house again. Find excuses, we're going to run errands and I need daughter with me, why don't you invite your friend to go with us?
Turn it around. Then you have complete control over the girls interactions and what's going on.