Hair is the key symbol in your dream. Here's a link to its definition on this site:
hair
Given the waking life background of your dream (thanks for providing that!), the fact that your step-daughter would disparage your hair and recommend that you cut if off, is consistent with your experience and feelings about her.
Dreams are expressions of your feelings about your waking life. And, feelings in dreams are never disguised, so how you felt IN the dream is how you feel about the subject of your dream in your waking life. You didn't say how her remarks and behavior made you feel, but I can imagine that they made you feel disrespected and diminished. The good news is that you probably already know that. That's how your mind & heart chose to express it in your dream.
Hang tough and stay steady. Doing so will provide an important foundation for her as she matures. As she does, so will your relationship. When dreams of your step-daughter evoke different and more positive feelings, it will confirm that your relationship has turned the corner.
May it come quickly! Good luck!