It’s unfortunate that what should be a helpful discussion has turned into a power struggle. Your mother does have a point. Your daughter has already lost her original family with the divorce. If you move, she will be facing the loss of her grandparents who have provided some stability and an extra dose of daily love during a difficult time.
What you see as attempts to “control” you may in fact be a desperate effort by your mom to preserve the kind of relationship she has with her granddaughter. What you see as a big step forward is a big loss for her. Is it possible that she doesn’t experience empathy from you for her feelings? Are the two of you able to calmly talk about how to best support the child as well as the adults in another transition?
My suggestion to you is that you stop seeing this as a win-lose battle with your mother. You both love your daughter and have the best interests of the little girl at heart. Invite your mother to a session with the therapist to talk about how to help you move on with your life and at the same time keep the strong ties with your parents that have been a lifeline for both you and your little girl.
I wish you well.