Definitely took the wrong approach. Think of it this way:
-You absolutely want the child to decide on her own. You see this as your right to decide because you are her father.
-She absolutely wants the child to have the church an active presence in her life. She sees this as her right to decide because she is her mother.
Who has more right over their child?
-You think she is being a bad influence on the child.
-She thinks you are robbing the child of something very important.
Can anyone truly prevent the child from choosing for herself? Is knowledge of religion truly without value even outside of itself? If you do not forbid her from teaching the child religion, would she be fair and allow you to also teach the child rationalism?
Really, your actions thus far, even as right as they may be in terms of influence upon the child, have been marred by insecurity, double standards, and belligerence. Religion also clearly has the upper hand in your life in terms of power, so fighting so directly and ultimately is ruining things for you. You need to come around and try to negotiate an "open borders policy" in regard to conversation with each other as well as the teaching of your child.
If you are confident that reason stands for itself, you can know your little girl will someday have the capacity to see the failures of religion. If your girlfriend has confidence that God is more powerful than the mind of man, she should have confidence that he will call her heart unto him. Ultimately, your daughter will choose what she does. If you can negotiate this sort of agreement now, your girlfriend will likely be more inclined to respect your daughter's autonomy rather than restrict her lifestyle when it inevitably differs from the archaic rules of the church.
That said... your father's response was FUCKED UP. Really sorry to hear about that. However, your response to that response, as wounded as it may have been, was fairly immature. When I became an atheist, some of my friends initially felt really betrayed, even ones who were used to dealing with unbelievers. Yet, because in conversation I guided them through the history of my experience, how the sense of God left over time and eventually the memory of it, my unanswered questions, and my inability to piece together a concept of God that is coherent, and things like these, they then understood where I was coming from.
So, watch
this and
this try to understand the power it still holds over them and gain some empathy for that, return to them more reasonable and more open, and don't get worked up just because they do. You are their son. They aren't hating you. That's not what it is.