You need to talk to the teacher. You can't expect this to get fixed if no one talks about it.
I hate to say it, but my daughter is the bratty/mean girl in her first grade class. This is not something the girl's parents don't know about. And if they're like my family, it's not something that they're ignoring. Believe me, this child keeps me up at night worrying and trying to figure out why she's like this. I talk until I'm blue trying to get her to understand that it's wrong to treat people the way she does. I've tried so many different discipline styles, we did play therapy when she was a toddler, she has a counselor now. She just is this way. That doesn't mean it's okay and that doesn't mean that you should allow her to be mean to your kid, but please don't be so sure that her mom's not turning away from you out of embarrassment and pain.
As a teacher I think it is sometimes helpful to say "several of the parents have complained about ....." It tells the parent of the difficult child that it is not just the teacher noticing problems about the child but other adults as well. We cannot "complain" about a child, only offer concerns and suggestions. To be told your kid is the one parents are complaining about sends quite a message, and usually the problem kid is very unhappy and needs help learning to be social. You should talk to the teacher and advocate for the school counselor having friendship groups to teach social skills- the poor kid is clearly not going to learn it at home.
We tried the “killing her with kindness” and it was not a success, so no, two wrongs dont make a right. This is why I am asking for advice. Clarification: my daughter has told me things that this girl has said ON and OFF for a few months. They are not all directed at her. I am being an advocate for my daughter, YES I have told her to tell the teacher and she has. Then, a few weeks go on with no reports of nasty comments and then another episode of something towards my daughter or another student. Do not judge ME as a parent. I am protecting and advocating for her I just wanted some “helpful” suggestions.