What does this relationship reveal about both emily and her father as characters.

I'm unclear about your question.  If you are asking what is their relationship like, it would be one that reveals the power relationship between the Southern "lady: and "gentleman."He, as we see him in the tableau, represents the paternalistic, authoritative southern male, dominating his daughter, Emily, who, in the background, appears submissive.  He holds a whip and wears boots, she wears white. Much of Emily can be explained through this original relationship with her father, which she does her best to break out of through Homer, whom her father would have hated, and then by killing Homer when he seemed to want to leave her.