This is a great question to consider. I suppose when we think about the central conflicts of both stories, we need to think about the way in which the conflicts occur between two family members. In "The Yellow Wallpaper," for example, the conflict is clearly between the narrator and her beloved husband, John, who clearly feels that he knows what is best for his wife and ignores any attempts of his wife to argue otherwise:
If a physician of high standing, and one's own husband, assures friends and relatives that there is really nothing the matter with one but temporary nervous depression--a slight hysterical tendency--what is one to do?
The way in which the narrator repeats this phrase, "What is one to do?" clearly indicates the conflict and the way that she disagrees with this diagnosis.
In the same way, the conflict in "The Rocking-Horse Winner" is between the mother and her son as Paul is driven to ever-greater lengths in his efforts to win her love, affection and approval. Note how the mother is described in the opening paragraph of this tale:
Nevertheless, when her children were present, she always felt the centre of her heart go hard. This troubled, her, and in her manner she was all the more gentle and anxious for her children, as if she loved them very much. Only she herself knew that at the centre of her heart was a hard little place that could not feel love, no, not for anybody.
Paul is thus driven to engage with supernatural powers in his attempt to gain luck or money and thus gain his mother's love and affection.
Of course, the other massive similarity between the conflicts of these two stories is the way in which the conflicts drive the narrator in "The Yellow Wallpaper" to complete madness because of her husband's refusal to take into account her feelings, and Paul in "The Rocking-Horse Winner" to his death as he is inspired to embark on one last frenzied ride. Conflicts between members of a family are shown to be potentially disastrous things.