Have you ever really hated one of your kid's friends?

I typically don't post, but I find myself at a crossroad with this. I'm currently newly pregnant and finding my filter to be very hit or miss. But today I bit my tongue instead of making a child that doesn't belong to me cry.

My eldest is 10, she's a bit of a strange one in the way she isn't in to what most 10 year old girls are. I don't see the issue with this. She's a really good kid (minus the typical kid stuff when it comes to chores). But she has a problem when it comes to making quality friends (though she has a couple of them whom I adore). This one little neighbor girl is definitely the worst. My daughter is so concerned about being her friend that she is almost spineless when it comes to her. This girl is a perfect embodiment of what is wrong with the world today. An entitled little brat. She treats my daughter with zero respect. Of course as a mom, I've tried to tell her the things that this girl does (ranging from name calling, to bullying, to making my kid feel worthless because she doesn't have everything that this girl does, etc.) is not okay. Now my kid is acting just like this girl, to impress her, and also basically being a coward and doing what this girl says even if she knows it's wrong so that she can maintain this "friendship". I've honestly had it with this girl. She's rude, has no respect for authority even from her parents, and is just a bad egg.

So how do you mom's deal with this? Because this morning I was seriously about to lose my temper, and make this kid cry. Then tell her never to come back because she's not welcome here. I didn't do that because I'm an adult and I'm not going to be rude to another person's child. Not only that, but it's not the example my kid needs to see from her mom. Im just at a loss and counting down the days until this kid moves away.