@nathanstrong I figured there was more to the story. That's why I try to withhold judgement unless someone is doing something obviously harmful, which you aren't. Obviously, you're going to do what you feel is necessary no matter what the Internet thinks, but I just wanted to tell you you aren't crazy and this should be a discussion and not a pile-on.
I agree with some other posters here, that you should consider disabling multiplayer or at least chat. As an older black gamer, I still usually disable chat because of the frequency of the actual n-word. Being Black, Latina, and a girl, my daughter is only going to game online in highly moderated spaces
One other suggestion is that you may want to record something time-stamped asking your kids to explain what they think the n-word is. I know if my daughter came home from school and said somebody said she was the n-word, I would have trouble believing that it meant something else unless some kind of proof existed.
As an aside, me and my siblings weren't allowed to call each other stupid or other insults. I'm the youngest and approaching 40, and we still are very close and have never had a fight where we insult each other. Insults are still at the bottom of my toolbox when I disagree with anyone, even online. Me and my wife of 8 years also only argue with love and zero insults. I'm not special or anything, but I think you can have a long lasting effect on your kids by teaching them self control even when they're mad.