The relationship between Sylvia and her grandmother is a good one. Mrs. Tilley seems to possess a better understanding of Sylvia and what makes her happy than Sylvia's mother did. Sylvia's mother, it seems, had told Mrs. Tilley that she was "'Afraid of folks'" when Mrs. Tilley made the "unlikely choice" of Sylvia from her daughter's houseful of children. However, Sylvia had "tried to grow for eight years in [the] crowded manufacturing town," and only seemed to come "alive" when she moved to the farm. Mrs. Tilley clearly saw something in Sylvia that no one else had, and her choice was a great one.
It seems that Mrs. Tilley didn't have as much time with her son, Dan, as she would have liked. She tells the stranger, "'Dan an' his father didn't hitch, -- but [her husband] never held up his head ag'in after Dan had dared him an' gone off.'" Therefore, we can understand that Mr. Tilley and his son, Dan, didn't get along very well, and, at some point, things came to a head and Dan left home, never to return. Now, however, Mrs. Tilley gets to have a second chance at a relationship with someone who "'the wild creatur's counts [as] one o'themselves'" since "'Sylvia takes after him.'"