Hello Mal,
Your daughter is fortunate to have identified her abadonment issues this early in life. Even though you are the mother she was meant to have, there is an energetic attachment that exists between a biological mother and her child. Her need to be best and first is her way of being worthy and deserving of acceptance and your love, specifically, and others in general.
EFT is definitely the way to go. I would say to you and any parent reading this post that seeking out guidance from an experienced and competent EFT Practitioner would be wise. There are times, when working with loved ones, that your own feelings surrounding the issues are too emeshed and you wind up 'stepping into' each others energy.
You know that you are a good mother and that her issues with her biological mother do not diminish the love and bond she has with you, her true mother.
Happy Tapping!
Nurse Crilly