Why doesn't Miss Emily speak to her family in Alabama? Because they didn't come to her father's funeral? Because there was a dispute over an aunt's estate? Because she is seeing a Yankee?

From the text:

She had some kin in Alabama; but years ago her father had fallen out with them over the estate of old lady Wyatt, the crazy woman, and there was no communication between the two families. They had not even been represented at the funeral.

Answer: Because there was a dispute over an aunt's estate