In "The Story of an Hour," how is Mrs. Mallard both the protagonist and antagonist?

After hearing the news of her husband's death, the first reaction that we get from Mrs. Mallard is that she "wept at once, with sudden, wild abandonment," which seems to indicate that she was horrified at the news, and miserable as a result of it.  In this reaction, Louise is playing the protagonist; she is reacting normally, we feel for her grief, and get wrapped up in the misery that she must be feeling.  Our hearts go out to her, and we automatically rally to her side, championing her cause.  That is typically the reaction that the protagonist, or "good guy" in the story gets.  We like them, or at least are on their side.

However, as soon as she enters her room, she experiences a bit of a change of feeling.  The story states,

"There was something coming to her and she was waiting for it, fearfully...She was beginning to recognize this thing that was approaching to possess her, and she was striving to beat it back with her will."

Here, she undergoes a serious change.  There is a feeling overcoming her, almost like a normal person who changes into a superhero or a villain.  It is a feeling that she is dismayed by, but can't fight back.  That feeling is freedom, elation, and joy that her husband is dead.  Once she realizes what that feeling is, and how powerful it is, she surrenders to it, rejoicing in the fact that

"There would be no one to live for during those coming years; she would live for herself. There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature."

So, she goes from the grieving widow that we feel bad for, to a heartless creature who is rejoicing in her husband's death.  Whether we empathize with that feeling or not, it is quite a change, and all of a sudden she is a woman feeling "monstrous" emotions, and for some, it might feel like she has turned into the antagonist, or the "bad guy" of the story.  I believe that was what your question was referring to-Mrs. Mallard is both the protagonist AND antagonist in the story, because she stands on both sides of the major event of the story, her husband's death.  I hope that those thoughts help a bit; good luck!

What is the nature of conflict in "The Story of an Hour" and who is Mrs. Mallard's antagonist?

The conflict in Choplin's classic short story can be considered a Woman vs. Society conflict, where Louise Mallard struggles to overcome the oppressive aspects of a patriarchal society, which prevents her from exercising personal agency or embracing independence. Choplin's story is set in the late 19th century, which was a time when women had little to no rights and society expected them to remain docile and obedient to their husband's will. Mrs. Mallard was expected to remain indoors, carry out her husband's wishes, and perform necessary domestic duties. Although Louise Mallard loves her husband, she resents the submissive, oppressive nature of her restricted marriage. Louise Mallard desires to experience autonomy and live completely for herself, which is something that institutional marriage and society prevented at the time. Therefore, Louise Mallard's conflict is with society's expectations of married women and her struggle to experience independence in a male-dominated society.

The main conflict in "The Story of an Hour" is character vs. society.  Mrs. Mallard's adversary is not her husband, as some might argue, but society, due to society's expectations for right female behavior as well as marriage.

First, Brently Mallard was a good husband.  Mrs. Mallard "knew that she would weep again when she saw the kind, tender hands folded in death; the face that had never looked save with love upon her [...]."  She doesn't take issue with him, in particular, but rather the institution of marriage, in general, and what it meant for the woman.

She feels a "monstrous joy" because, from now on,

There would be no one to live for her during those coming years; she would live for herself.  There would be no powerful will bending hers in that blind persistence with which men and women believe they have a right to impose a private will upon a fellow-creature. 

The joy is somewhat monstrous because it comes at the expense of her husband's life; however, though monstrous, she does happy because she recognizes, as she says, that she can now be "'free, free, free!'"  In marriage, a woman of this period loses her identity as an individual; she becomes someone's wife, and her husband is legally entitled to make any and all decisions of importance.  Her duty is to acquiesce to his wishes.  She would likely not have married had this been a viable social option, but it was not during this era.  This wasn't the arrangement just for her marriage, but for all marriages.  Even though her husband was kind, she was still required to allow him to "live for her."  As someone's wife, she could not live for herself.  As a widow, she will now have that right.  Without the social expectations surrounding marriage and the prescriptions for her behavior within that institution, Mrs. Mallard would have had no adversary.