Mom Undermining My Parenting

My teenage daughter now has a flip phone because she was bullying this girl on Facebook and telling her to kill herself. I ended up being called into the school because of it. The girl would block her and my daughter would make another account to harass her and the poor girl started self harming. My child showed no remorse and kept using the excuse "I wasn't the only one bullying her" and how she finds the girl annoying. She's been grounded, has no phone except her flip phone and has been made to come straight home after school. Well my mother bought her a new iPhone. I told her she can't have it and my mom said I'm being stupid and that the other girl needs to grow up. Its not ky daughters responsibility if someone starts cutting themselves over a few mean words. Shes saying all this in front of my daughter and my daughter is just smiling. Shes flat out undermining my parenting in front of her and making her Think bullying is okay!!