The main differences between these two short stories in terms of the relationships that are portrayed is the age difference and then the gender difference. In "Barn Burning," Sarty is of course Abner's son, and thus separated by him through age. As a son, he is expected to be faithful to what Abner calls his "blood":
You're getting to be a man. You got to learn. You got to learn to stick to your own blood or you ain't going to have any blood to stick to you.
Sarty's rebellion against his "blood" shows the extent to which he obeys his conscience rather than the oppression of his father, who supports his iron rule of his family with violence and fear.
Mrs. Malard in "The Story of an Hour" is of course a married woman, and thus the relationship explored is very different, as her husband is of a similar age. The power imbalance that is portrayed is therefore a result of gender rather than age difference. Note how Mrs. Mallard thinks of her marriage when she contemplates the freedom she has now that her husband has died:
There would be no powerful will bending hers in that persistence with which men and women believe they have a right to impose a private will upon a fellow-creature.
Even though the relationship in this short story is very different, the same issues lie at the heart of it, as Mrs. Mallard suddenly finds herself delighting in the freedom that she can now experience as a widow, no longer having to play the role of a married woman.