Would you trust your friend after you caught her talking badly about you?

Talk to her about it. Tell her that you're not dumb to not know that she's been talking bad about a lot of her friends. Confront her about it. To be honest, I wouldn't trust her for the time being, it's just not safe. Take some time to build up the trust again, only if you know if she's worth the keep. If not, fuxk it. Just put her aside. I'm sure you deserve a better friend. So yeah, just confront her about it.