Hello...I am sorry to hear about the problems that you are having with your grand-daughter. If she is a teenager, it is completely normal for her to manifest all sorts of up and down feelings as she tries to find, assert, and develop her independence. Relationships with family is of decreased importance and she will be more concerned with friends and the social scene.
To assist with the problem, I would like to suggest that the situation is brought to your daughter's attention if not done already. Your daughter needs to be the one to tell your grand daughter that she needs to be more respectful towards you. You can be present during that conversation if so desired. Your grand-daughter needs to open up and explain why she acts the way she does. Your daughter needs to ask your grand-daughter what can be done to improve the relationship between you and her. You need to see where she is coming from and how she truly feels. Maybe there is a deeper rooted problem that you are not even aware of.
I was wondering what the relationship is like between your daughter and your grand-daughter. Hopefully, your daughter is taking the time to strengthen that relationship.
What you can do is to continue to be the loving and supportive grandmother to your grand-daughter. If she shuns you away, never show signs that you are upset or hurt. She is trying to be the controlling one. You cannot control your grand-daughter but you can control your own reactions to her .
Hope this has provided some insight. If you need more advice, just ask.