Friend or Mother

My life seems to be doing a tango with these two roles of my life...in many ways.

1.) Can you be a good friend and a mother to an old friend that isn't one?
Yes, but it can be tricky.
2.) Can you mother your friends? and is that not so good?
Yes on both accounts.  I am guilty of mothering everyone.
3.) And this is the big one: Can you be friends with your mother?
I so badly want to be, but I do not think that my mom and I will have that relationship.  I have point-blank asked her, "can we be friends?" And she said, "No, I will always be your mother, and I don't want to be your friend."

My mom and I have always had a more difficult relationship.  She says it is because we are so much alike. I always thought that was untrue, until now.  Because we are so alike, she wants to change me into a better version of herself.  To fix all of the faults she sees in the both of us.  I get this feeling, but I don't like it.  While I don't like that, I also do not like that we are so alike because I don't want to do the things she does, I don't want to have her exact life.  So part of our fighting is me rebelling against being "like her"...which probably makes me more like her...It is a vicious cycle.

My mother and I will always have a difficult relationship because I will want to please her and be her friend and more than just her daughter, and she will not want those things.

My question to the universe and my prayer to God is "can you be friends with your daughter?"

I want to be a friend and a mother to my daughter.  Not the Gilmore Girl version...that is weirdly co-dependent.  But I want to be someone my daughter trusts, comes to for advice and not judgement, can feel safe with me and have fun too.  I do not want to be the mom who tries to be a teenager friend...I will not try to be cool (I have never been that)...but I so badly want to find that balance.

Do you have that relationship with your mom? your daughter?  How did you get it?