My sister's 9 year old "daughter" hates me over something from years ago.

My sister is 25 years old and I'm 21. Three years ago she adopted a kid from Sudan with her fiance. Our family is very conservative and although we don't judge, me and my parents did show a little displeasure. One night we all got into a fight and I wrongfully referred to the child as the little n word baby and my parents were calling her worse. I had no idea the girl was in the room right next to us. When we left the kitchen and went back into the living room, the girl was just staring at the ground and she went outside to sit on the front porch. I didn't think that she was hurt behind us because well, she's 6. I doubt she knew what we were talking about or what any words meant. But now 3 years have passed and she's 9 years old. Every time I try to talk to her, bring her a gift, or play with me she just looks at me and goes back to whatever she was doing. She'll accept my gift and give me a quiet thank you but thats about it. I have been doing everything I can to show this girl that I love her and she's not letting me in. I'm slowly giving up and I don't know what to do. I just don't see how a 9 year old can hold such a grudge or how a 6 year old even understood what we were saying. I just feel like I could use this whole situation to teach her a good life lesson that people change.

Guys please. I put quotation marks so people who are reading the title catch on that she's adopted.

Guys, I can't apologize enough to her. I have apologized every time I see her for the past years. You guys are cyber bullying me but I'm crying out for help here. I was a 17/18 year old girl who was following her parents. I have changed and am still changing. I WANT to be in her life. I want her in my life. If you guys are gonna keep bashing me then why am I even looking for advice.