Louise Mallard's external conflict is with society, not with her husband. In fact, she acknowledges 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, fixed and gray and dead.
Her problem is with marriage and the fact that she, as a woman, has practically no rights within a marriage at the end of the nineteenth century. Legally, her husband has the right to make all of the decisions for their family, and she has had to compromise, apparently, in ways that have led to the narrator's sense that Louise has experienced enough repression to create the lines on her face. Now, Louise thinks,
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. A kind intention or a cruel intention made the act seem no less a crime as she looked upon it in that brief moment of illumination.
Now, she can exercise her own will. Her husband was not a bad one, but society determines the ways in which husbands and wives are supposed to act, and her prescribed role is clearly not something that Louise has ever been comfortable with. She does not seem to want another husband, because she does not want to ever feel controlled again.
Her internal conflict is brief. Initially, she seems to have little sense that she is actually feeling relief—relief that she will no longer have to "live for someone else" rather than herself. She seems to try not to feel this way, at first. Soon, however, she begins to understand:
There was something coming to her and she was waiting for it, fearfully. What was it? . . . She was beginning to recognize this thing that was approaching to possess her, and she was striving to beat it back with her will—as powerless as her two white slender hands would have been. When she abandoned herself a little whispered word escaped her slightly parted lips. She said it over and over under her breath: "free, free, free!"
In short, Louise relishes her freedom, not from her husband, necessarily, but from her marriage. It was marriage, not the man himself, that caused her problems. Once Louise understands how she is truly feeling, and why, her internal conflict seems to resolve.