If you see Edna as the protagonist and her attempts to define herself independently of husband and children as the mian conflict, it would make sense to me to call her husband, Léonce Pontellier, the antagonist.
For me, one of the most telling scenes in the novel that shows this relationship is in chapter one, summarized in the enotes study guide as follows:
Leonce lights up a cigar and sees his wife Edna walking up to the cottage with Robert Lebrun. He reprimands them for bathing in the heat, and gives back her wedding rings, which she had taken off prior to going to the beach.
Léonce is certainly the one with whom Edna has muted and open conflict, and this conflict shapes pretty much the whole story.
Of course, even a short novel is a novel, with many characters and plot lines. There may not be a single antagonist in The Awakening.
Kate Chopin's characterization of the potential male antagonists -- Leonce Pontellier and Robert Lebrun -- seems to indicate that the antagonist is not a person but is, instead, the larger society in which Edna lives, its expectations, and its norms. Chopin seems to critique not individuals but institutions like marriage that limit women's freedom. If there is one individual that we might say could serve as an antagonist, the closest would likely be Edna herself, as much of what is dramatized in the novella is Edna's internal conflict.
While Edna does have verbal altercations and what we would term "conflicts" with both her husband, Leonce, and her potential lover, Robert, Chopin makes it clear that neither Leonce nor Robert is a villain, but both are merely products of their time and place. They are both upper class Southern gentlemen. They expect their wives to behave in particular ways. They perform what society has deemed as their duties toward their families. Leonce is considered a model husband by the other women in the Pontellier's social circle; however, we see very little interaction between Leonce and Edna. Early in the novel, when the family is vacationing on Grand Isle, Leonce goes to the club for dinner only to return much later to chastize Edna for not attending to one of their "sick" children. He has not spend the evening with the family and accepts no responsibility for the children's care. He wakes Edna to scold her and to insist that she do something. This could be considered antagonistic behavior, but Edna herself thinks that it is unusual for her to cry or have any emotional reaction at all, as scenes such as these "were not uncommon in her married life." She recognizes that "They seemed never before to have weighed much against the abundance of her husband's kindness and a uniform devotion which had come to be tacit and self-understood." While over the course of the novel, Edna and Leonce do argue as Leonce attempts to tighten his hold over his wife, who begins to act out and behave erratically (such as when she leaves the house in New Orleans when she is supposed to be waiting on callers), it is clear that Chopin does not want to paint Leonce as a particularly villainous individual or even as a bad husband; he's simply the typical husband of the time. The problem is with the institution of marriage and the social mores that govern women's behavior, not with this one man who seeks to uphold the gender norms of the society in which he was reared. While Robert is younger and seemingly more carefree, when it comes time for Edna and Robert to confess their feelings for one another, Edna is shocked to hear that he wants to make her his wife. Over the course of her awakening, Edna has come to realize that she feels oppressed by marriage -- as an institution --(note how she reacts to her sister's wedding) -- and even though she loves Robert, she does not want to "belong" to any other person.
That said, if there is an antagonist in the form of a person, it may be Edna herself. She struggles throughout the novel to understand and to articulate the feelings she has toward her position "in the universe," as the narrator notes early on. She is torn between the side of her that has been brought up to believe in strict gender roles and propriety and the newly-awakened side of her that wants to simply act and be as she sees fit (this is Emersonian -- she does not feel the need to be consistent and acts on whims and impulses and does not apologize for it). Edna realizes that she has always understood that she, and by extension, other women, live different lives on the surface than what is true to their selves under those socially-appropriate surfaces. However, it is only during the course of the novella that her rebellious side begins to act out and to defy the conventions of her time and her society. Eventually, Edna's decision to drown herself could be seen as her inability to resolve these two conflicting internal voices or forces.