How does Mrs. Mallard respond to her husband's death at the beginning of the story?

When Mrs. Mallard initially hears the news about her husband's death, she accepts the tragic information and immediately bursts into tears. Mrs. Mallard experiences a "storm of grief" and cries heavily into her sister's arms before she enters her room to be alone while her sister and Richards wait in the living room. Mrs. Mallard's sister, Josephine, fears that her sister is harming herself inside her room. However, Mrs. Mallard is calmly beginning to notice the beautiful, peaceful spring day from the view out of her window. As Mrs. Mallard sits alone in her room, she comes to the realization that she will spend the rest of her years independent and free from the oppressive influence of her husband, which is a relieving, exhilarating feeling.
Mrs. Mallard's initial reaction to discovering her husband's death is one of acceptance. Unlike many wives, Mrs. Mallard is not shocked or paralyzed by her husband's death. She also reacts by crying hysterically before retreating to her room to be alone, where she contemplates the positive significance of her husband's death.

At the beginning of the story, when Mrs. Louise Mallard first hears the news about her husband's supposed death in a railroad accident, she does not respond in the way that would be expected of a typical wife. The narrator says, 

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.  

After Mrs. Mallard has cried herself out, she retreats to her bedroom alone, and she will not allow anyone to come with her. Although her sister, Josephine, fears that she is doing harm to herself, Mrs. Mallard is really coming to understand that she is now free. It's not that her husband was a bad one—he "never looked save with love upon her"—but the very fact that he was her husband meant that he had the legal right to "bend [her] will" to his.
Therefore, Mrs. Mallard's first reaction seems to be one of relative acceptance, as opposed to shock, and she cries hard. Soon, though, she realizes that the death of her husband, while sad, actually means that she will get to live as a free woman for the rest of her life.