Why does Joanna eat in the kitchen?

This is a very good question! If Joanna is part of the family, why doesn't she eat with them? Why does she eat with the servants in a different room?

Sadly, her family treats Joanna as if they're ashamed of her because of her physical deformity. Look in Chapter 24 when Joanna is being discussed. We find out that she's about fourteen years old, and that she has a hare-lip. It means that when she was born, her face was slightly deformed. For that reason, people actually call her "hare-lip" or "the hare-lip."

In fact, throughout the rest of the story, the narrator refers to her mostly by that cruel nickname.

Then we find out in Chapter 26 about where she eats:

"And when it was all done me and the hare-lip had supper in the kitchen off of the leavings, whilst the others was helping the n*****s clean up the things."

Although we're never told exactly that she eats away from the family because they're ashamed of her abnormal appearance, that's probably exactly what's going on. We know that people who have a cleft palate, especially if they're young, might have a harder time eating neatly, so any messes might inconvenience and embarrass her family.

Notice, too, that she eats the leftovers; she doesn't even get her own full plate like the rest of the family.

Considering how Joanna's family treats her differently because of how she looks helps you understand the larger issue of discrimination that the novel explores.