Personally I'm not very religious. However, in my humble opinion not helping your child when she has the tools to help herself is not the same as writing your child off completely. I have tons of times when I don't want to talk to people/children. on the other hand I don't stop loving them I just stop the drama by stepping away from it. There is a difference.
You aren't writing your child off and saying they don't exist or that you don't care. You are still a loving parent you just aren't doing what she wants you to do. God doesn't want us to harm ourselves in order to help others simply because they wont help themselves.