While the theme of Kate Chopin's "The Story of an Hour" is certainly a subjective one--female self-assertion--the point of view is third person limited. But, Chopin does manipulate this objective point of view with subtle skill. At first Mrs. Mallard (notice the affected distance created by using this formal title) is incapable of assessing her situation. But, after she retires to her room, and becomes aware of her emotions, the reader begins to apprehend her character. However, when she returns downstairs, the reader is cut off from Mrs. Mallard's thoughts.
Thus, the subjective communication of Chopin's sympathies is very surreptitious as it is shadowed in the reportorial passive voice. This use of the passive voice in so many of her sentences also contributes to the subtlety of the theme. In an essay by Madonne M. Miner in The Markham Review, the critic contends that the language of the story keeps the reader distanced from Mrs. Mallard's "possession of self" until the end when Brentley Mallard appears in the doorway and Mrs. Mallard dies "of the joy that kills."
Miner contends that as "an affective stylist, Chopin reveals asubtle movement in the reader toward doubt" with her use of passive voice which seems objective, but does not actually name a subject of the action. For instance, the very first sentence creates doubt in the reader who cannot be positive about what "a heart trouble" means. First of all, the addition of the article a set up doubt, then there is great care taken by Chopin to keep the reader from know who has made this diagnosis of Mrs. Mallard's heart.
The use of the passive voice always connotes a diminishing of power of the doer of the action; this structure, by its nature, parallels and suggests the diminished power of Mrs. Mallard herself. The reader, then, wonders if there is not a more complex layer of meaning in the masterful story of Chopin who withholds responsibility for the action through third person limited point of view, yet creates the subjective possibility of her them at the same time. Thus, the contention can be made that the writer's position is both objective and subjective.
Your question concerning Chopin's "The Story of an Hour" deals with the narrator's tone and manner of presenting the story.
Objective, as you use it, refers to the point of view of the narrator. An objective narrator relates only the details of the story without interpretation or judgment. Fiction can be objective, but this story is not.
The narrator's attitude toward the protagonist in the story is sympathetic, and she interprets her character with sympathy. This is subjective.
Mrs. Mallard is presented in a positive light. If the work were objective, she would be presented in a neutral light. For example, the character is "young, with a fair, calm face, whose lines bespoke repression and even a certain strength." "Repression" is an interpretation and judgment of the lines on the woman's face, and indicates that as a wife--even as a wife to a relatively good man--she suffers repression. And "strength" is an interpretation, also, as well as a judgment.
Interpretation and judgment on the part of a narrator demonstrate that a story is narrated in a subjective manner.
Notice that I have interpreted your use of "writer" to mean "narrator." We can't, strictly speaking, pretend to know what is in a writer's mind at the time of writing. We try to refer to the narrator, rather than the writer. At the same time, looking at this story and other works by Chopin, you are probably safe in saying that Chopin, too, is subjective in her approach to a woman's place in marriage and society. She is a strong feminist writer, and often reveals the claustrophobic-like roles women are forced to play in society.
The story "The Story of an Hour" is subjective. Material that can be proved as a fact in literature is usually objective in literature. The story is fiction and the characters may be true to the error in which they would have lived if they were real, but they are made up to demonstrate an irony of events.
The relatives go to the woman to comfort her when they believe that Mr. Mallard has been killed in a train accident. Mrs. Mallard locks herself in her room and begins to have dreams about being free from the constraints of being a woman. The story in itself is subject to the readers own opinions about the ending and circumstances.