How can I stop a hateful woman from spreading lies about my 17 year old ?

the best way to stop someone from spreading lies about someone is to talk to them privately and see why they are doing it.

Speak to her in a calm manner explaining how the lies makes both you and your child feel. Also explain how the lies have consequences and what those consequenes may be. Often when we approach someone and confront their actions in a calm and communicative way, it can be very effective.

Try to resolve the issue with her, ask what happened. Maybe if she feels heard or that you attempted to resolve it will curb her need to consult with more people about what she belives happened

I think by been stern, yet, kind confront the woman for her misbehavior by acting out against my 17 year old. Physical fights doesn't solve anything, really it adds more fuel to the fire. Instead, I would either confront her calmly or leave the situation so it wouldn't escalate. I personally once experienced someone insulting me by discrimination slurs and I was livid because of it. But I kept my cool and walked away because the whole point of saying it was to get my reaction. I didn't gave them the satisfaction and came out victorious while also letting them reflect on what they just did. Similar to this situation, it's difficult to leave but usually its one of the best options

You can't. People love to talk about other people, especially teenage girls. You can't control what others do or what others say about your daughter. However, you can control the way you and daughter handles it. You are her mother. You can give her tools for her emotional toolbox that will make her confident and strong willed. You can control how much time she spends on social media (which I'm assuming most of the gossip is occurring on). You can spend more quality time with her and ask her how it makes her feel and also ask her what solutions she thinks are best. Most importantly, just be there for her. Maybe figure out what these "lies" are and get down to the root of the problem that is inspiring these rumors. Feel free to show her this message.