The internal and external conflicts in this story must be inferred from what information we are given. There is a strong internal conflict in Mrs. Mallard, and one clear external conflict is with her husband.
Mrs. Mallard's internal conflict is between what she believes is expected of her in the way of a response to her husband's supposed death and what her genuine emotional response is. Over the course of an hour, she moves from shock over the loss of her husband to feelings of joy and freedom. The conflict is between the societal expectation she has conformed to all of these years with her husband and her own needs and desires. There is nothing in the story to indicate that she has ever expressed her wants and needs in the marriage, yet she has repressed these over its course. It takes her an hour to resolve this conflict, with a gradual awakening to the idea that she can now embrace her freedom, no longer repressing her essential self.
All that we know of the marriage is through Mrs. Mallard's internal dialogue, in which she alludes to a marriage in which her husband has imposed his will upon her. This is an external conflict, a conflict between husband and wife. We have no real sense of how that conflict played out over the course of the marriage, but we do have a strong sense that Mrs. Mallard lost out to Mr. Mallard all the time. If that were not the case, Mrs. Mallard would not be so relieved. And if that were not the case, Mr. Mallard's "resurrection" would not have killed her.