Help with teenage daughter

I am torn between parenting (correcting my daughter) versus coaching (love her anyway). As a mom, I feel responsible for correcting my daughter to help her grow into a responsible human. BUT it seems like many of the coaching calls are about not trying to change anyone, but just to change my thoughts. Wouldn’t that mean I’d be abandoning my role as a mom?

example: she was talking back to me and criticizing her brother. she said we shouldn’t excessively celebrate his bday on his bday. I asked her to stop talking back to me. my T: she is rude. my f: frustrated. A: I asked her to go to her room after it escalated. R: I was rude/mean to her. I wasn’t the parent I would like to be which is to be more loving and understanding and see her as asking for attention instead of punishing her. I yelled bc it felt good at the moment BUT then I ruminated for days (too expensive!).