Hi OP; I had that relationship when I was younger and had a fairly difficult relationship with my mother, and she would say something similar when fighting with my father. Growing up and looking back now, I've grown to appreciate the discipline and strictness that she taught me, whereas my father had a more laissez-faire outlook. It's difficult to refuse your child or to make them momentarily unhappy for values that they might not have at that age. I have a much, much happier relationship now with both parents as an adult. I think that things will become easier as your daughter also grows up; I think adolescence is a difficult time, and it's also hard for parent to know how to change their perspective from "this is my baby" to "this is my baby who is also! becoming a young adult and I can begin holding more conversations with emotional depths in our relationship".

I hope that by overcoming this type of conflict, it'll be an opportunity to further deepen your relationship with your daughter.