Unfortunately, the family situation in "Barn Burning" is atrocious. Think extreme poverty, a tyrannical barn-burning father, constant moving, and zero respect in the community. What's more, all the relationships between members of the Snopes family seems so shallow, dysfunctional, and lacking in tenderness. By focusing on a complicated and painful relationship between a father and son who have different belief systems, this story explores the tricky problem of what to do when the needs of the individual are at odds with the demands of the family.
Sarty's brother is important to the story because he shows what Sarty would have become if he hadn't take matters into his own hands.
The fact that Sarty doesn't seem to have deep relationships with his mother and siblings contributes to his decision to leave home.