At what point in the story does the reader know the problem has been resolved in "Desiree's Baby"?
In order to answer this question, you first need to identify the conflict (or the problem) of the story. Though a very short short-story, "Desiree's Baby" presents more than just one simple conflict.
First, there is the mystery of the identity of Desiree, and of course, her partially black baby. Is there a slave in the ancestry of the baby's mother or father? This is the first problem.
Of course, Armand suggests and fully acts upon the assumption that Desiree must be the one who has brought slave ancestry into his family line, and rejects his son and his wife as a result. This creates the external conflict between Desiree and her husband, which outside of her leaving and returning to the home of her parents, goes otherwise unresolved. The only thing the audience knows of the "resolution" of this conflict is:
She disappeared among the reeds and willows that grew thick along the banks of the deep, sluggish bayou; and she did not come back again.
Though Armand "solves" his personal conflict, the bigger picture remains untold, as we never hear of Desiree again.
The mystery of identity, the primary conflict, is somewhat resolved in the final line of the story:
...our dear Armand will never know that his mother, who adores him, belongs to the race that is cursed with the brand of slavery.
The resolution comes in the form of showing the audience that Armand was wrong. However, the big picture ends in ambiguous irony. Chopin purposefully ends her story on an ironic surprise ending and leaves lose ends untied, most likely, to cause her audience to draw its own conclusions. It is clear the focus here is not on solving the conflict between the two main characters or even within Armand himself. Instead, the purpose seems to be to draw attention to a third, and more global conflict, which is that of the human condition and its propensity toward prejudice, hatred, and superiority.
Chopin is showing that a societal conflict exists in the context of the story, and does not present a resolution, likely because at the time she wrote the story, one did not exist. Some might argue that the conflict of human hatred and prejudice is one that will never be fully resolved.