Why was Mrs. Mallard's response different when her husband died?
I am not sure exactly what is meant by your question, whether you are asking how Mrs. Mallard's response was different from other women's in the same situation, or you are asking how her response changed over the course of an hour. Either way, there is much to be said.
The story actually makes a point of explaining that Mrs. Mallard's response was not typical of other women:
She did not hear the story as many women have heard the same, with a paralyzed inability to accept its significance. She wept at once, with sudden, wild abandonment, in her sister's arms. When the storm of grief had spent itself she went away to her room alone. She would have no one follow her (para. 3).
The author is suggesting that most other women would have been slow to accept news of their husband's death, too much in shock to absorb this news. Additionally, it is not likely that most women would have retreated and left the comfort of others under these circumstances. So, the author is telling us already that there is something unusual going on with Mrs. Mallard.
Over the course of the hour in which she believes her husband to be dead, Mrs. Mallard undergoes a transformation. First, we have her wild weeping, but then, as she sinks exhaustedly into her chair and watches the beauty of nature outside her window, another emotion creeps up on her, one she can scarcely recognize. What she comes to understand is that she is free. And it is the death of her husband that frees her. She is filled with joy, the joy that comes of knowing that she will no longer be caged, that she can be as free as the birds singing outside her window. She revels in this new emotion, at least until she discovers that her husband is not in fact dead at all, and her newly gained freedom is not to be. It is this change in her emotional state that actually kills her.
We cannot know to what degree other women would have had the same response, the joy of freedom, but we do know that women in that time had very little in the way of autonomy, with few getting an education or being able to work outside the home, with many having their spouses chosen for them and expected to be obedient to those husbands. So, perhaps there were other women who would have experienced the same sense of freedom upon a husband's death.
We do know that Mrs. Mallard's responses changed dramatically in just one hour, from wild, abandoned weeping, to quiet contemplation of the freedom outside her window, to a dawning recognition that freedom was a wonderful feeling, and finally, to the shock that killed her when she realized she was not free at all.