As your question implies, the central issue in Chopin's "The Story of an Hour" is not the marriage of Brently and Louise Mallard--although their marriage allows the larger theme to be played out--but the institution of marriage, particularly as Louise Mallard perceives it.
The story's plot, of course, can be stated succinctly--Brently Mallard appears to die in a train accident; Louise Mallard grieves and then has an awakening; Brently Mallard returns; Louise Mallard has a heart attack and dies. In between these events lies the tale, however, of a woman who undergoes a profound change and discovers, to her astonishment, that she has been trapped in a marriage that she hates, not because her marriage is particularly bad but because all marriages limit freedom.
Setting in fiction can either be important or unimportant. In "The Story of an Hour," the central event occurs in Louise Mallard's bedroom where she has gone to grieve. Her evolution begins because, as she is surrounded by familiar things, she begins to notice life outside her window:
. . . the tops of the that were aquiver with the new spring life. The delicious breath of rain was in the air. . . . There were patches of blue sky showing here and there through the clouds. . . .
The natural elements, immediately available to her, foreshadow the sense of new life and freedom that Louise Mallard will first attempt to "beat . . . back with her will," but her evolution has begun. The setting, her bedroom, is important to Mallard's growing sense of freedom simply because it provides the privacy with which to think quietly and allows her access to the natural signs of freedom outside her window.
This story is interesting, in part, because the central character, the protagonist, goes through a profound change, which we fully understand, in almost no time (an hour) and in a page and a half. In that time, we begin to understand the Louise Mallard does not hate her husband, but she feels trapped by marriage. At the same time, however, she does not seem to complain about her marriage in particular. After all, when she imagines seeing her dead husband in his casket, she imagines that she will cry when she sees "the kind, tender hands folded in death; the face that had never looked save with love upon her. . . ." The central theme, then, is not the marriage of the Mallards but, as we learn shortly, marriage as an institution.
Along the way to her exclamation that she is "[f]ree! Body and soul free!," the final statement of her evolution from trapped wife to free woman, Louise Mallard points out that marriage, even a good marriage, takes freedom away from both husband and wife:
There would be no powerful will bending hers. . . . A kind intention or a cruel intention made the act no less a crime as she looked upon it in that brief moment of illumination.
Louise Mallard's character development is central to the epiphany (a metaphorical light going off in her head) that marriage is prison for both men and women, and that the death of her husband--for whom she has grieved (for a while)--has unexpectedly freed her from a kind of bondage. Her reaction to this realization is an overwhelming sense of freedom, a freedom, however, that, like her life, is short.
Louise Mallard's mental and spiritual battle, then, has been waged against an institution that she views as inherently bad for both men and women. An accident of history--the belief that her husband has died--sets off a change of events that includes Louise Mallard's character undergoing a profound change and, as important, her realization that marriage as an institution is the cause of her underlying unhappiness, not her marriage in particular. Chopin illustrates two important themes in his very short story--1) a character's ability to evolve dramatically and convincingly and 2) the institution of marriage may limit freedom of will for both men and women equally.