I think you HAVE to get Dad in on this one. He must demonstrate that you are a family unit, not daddy and daughter against the world. I thought that the advice about the "contest" to see who could love mom the most was GREAT!! It may stroke his ego right now to feel he is the favorite, but that is not a good paradigm for the family to operate under over time.
HE must SHOW her, because she is small and telling is not going to be a affective as doing, that Mom is a part of everything that we do. He might start coming to you and asking your advise in front of her. Mom is great at this--Dad does this the best. ALL of us make the family. We love everyone, and everyone is our favorite.
Part of it is her age. You are sensitive because of you and your mom. Make that your issue, and DO NOT pass it on. Examine and truly evaluate what is not functional about you and your mother and try to fix it. You cannot always. But you can be darn sure your daughter is not raised in the same spirit that you were. We are not doomed to repeat the past. We are thinking functioning people and we can change it!
You are going to have to have some help. You are probably going to have to have a heart to heart with him and get it fixed.
He could say, for example, in the morning, "I was busy and I sent Mom to help you, she is good at it too!" Two parents is a how families are SUPPOSED to be for good reason. Everyone has different strengths and weaknesses.
My four kids know that Dad and I parent together, and the answer does not change if you go ask Mom if Dad says no, but they come to me about school and relationships, but I am lost in the world of sports, where my husband shines. He is also, be far, the most diplomatic of the two of us.
I hope this helps! Feeling that your young child hates you is not good. You can, however, fix it. As long as we breath we can fix it.