We've been together for 4 months now. To make this clear, my girlfriend also has a 6 years old daughter, and she often fights with me because I'm very close to my little sister (who is the same age as her daughter). She says that I treat my sister better than I treat her daughter. I mean, I do like her daughter and all, but of course that my sister is my priority. I've known her for 6 years and we're bonded by blood, whereas I've only know her daughter for 4 months. But she says that she and her daughter should be my priority, not my sister. She always demonstrated discontent right from the beginning.
I was almost 20 years old when my sister was born. Even though we are both children of the same parents who are still together, she was born at a time that my father was severely injured, so I helped take care of her like my daughter. Also, I was going through a major depression episode back then, so my sister was like a new light in my life. We've always been extremely close and always bought her stuff and took her out to have fun experiences. Unfortunately, my girlfriend doesn't understand that. She wants me to be the father of her daughter and put her as my top priority in life.
tl;dr: my girlfriend doesn't approve my relationship with my little sister because she thinks I should consider her daughter as my top priority.