We are not exactly told why Joanna (the youngest of the three Wilks sisters) does not eat with the rest of the family. I would assume that it is because of the way she looks.
We are told in Chapter 24 that Joanna has a "hare lip." This is what we would now call a cleft palate, a deformity that can significantly affect the mouth area. So I assume that Joanna is made to eat away from the family because they do not want to look at her as they eat.
We are never told in the story why she does this, but as the girl with the "hair-lip" she might be self conscious about her behavior. One can only speculate why, because there doesn't seem to be a proper explanation given in any Mark Twain documents about this particular incident. It could be to distinctly separate the children to give them greater personalities and individual identities, to make them more sympathetic to Huck, as he eventually retrieves their stolen money and he does end up telling the girls about the plans of the King and the Duke.