in what sense can this story be said to be about the difference between reality an appearance?

I'm not sure what you mean by reality. Berry is a black man, and Mrs. Osborn had been reluctant to hire him because of his race. He is overworked, underpaid, and he loves the children. Unfortunately, one of the children is injured while in his care.... and he is fired. Are you looking at the option that he was treated like a slave because of his appearance?

Berry is no other than a typical Negro who has been looked down on because of his race ever since. Mostly every single aspect of the story ties in with unfairness and racism. Despite the fact that Mrs. Osborn underestimated him from the beginning, the children themselves proved that Berry is capable in doing his job.The children loved and respected him. Appearance does not always make the cut, It's the true character or your original reality that lies within you.

berry said that when the parents come to visit, the children are treated nicely and food and prepared well (appearance)

but in reaity the children are not being taking care of very well they were badly treated . mr renfield just wants the money not to take care of the children.

how does the author prepare us for the climactic event of the accident and the subsequent dismissal of berry

how does the author prepare for the climatic event of the accident and the subsequent dismissal of Berry