What are the conflicts in Mrs.Mallard?

The primary conflict within Mrs. Mallard is the emotional ambiguity she experiences upon learning of the death of her husband. When she is told that her husband has died in a train accident, she goes to her room alone. Mrs. Mallard seems to experience some confusion regarding what it is she's feeling: "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." Then, "when she abandoned herself a little," she realizes that she will be "'free, free, free!'" At this point, she loses the look of terror that had been on her face, and she now recognizes 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 [...].  But she saw beyond that bitter moment a long procession of years to come that would belong to her absolutely.

In other words, then, Mrs. Mallard will mourn her husband, and it sounds as though he was quite loving and kind.  However, simultaneously, the knowledge that her life will now be hers alone to live as she chooses is such an incredibly compelling and welcome feeling. Although she does experience conflict regarding her husband's death, her feelings of relief that she will finally be free triumph over any sense of loss she feels.