I agree with the others, that last paragraph did you in. Up to that point, I was feeling sorry for you and everyone else involved. If the employee goes through life feeling that way, that's sad too. It sounds like you were trying hard to keep it together, but her comment put you over the edge.

Maybe... and this is a big maybe, when you are calmer, you could go back and try to explain to the employee that your anger had nothing to do with her color, and that you were very upset by the accusation. You never know, you both might feel better in the end.