A few things jump out at me in paragraphs 2 & 3:
"She wore black dresses . . [unlike] Mrs. Sol . . . she presented a naked white countenance to the fault-finding light of spring days."
The mother's white face above her night-black clothes makes her appear as a moon, esp. in comparison with Mrs. Sol. Like the actual moon (which regularly appears in the daytime sky, but is never imagined that way) she seems out of place in daylight. Her natural setting is darkness.
"brother Isaac . . . they had nicknamed him 'The Prince.'"
This would seem to identify them as Jewish. Perhaps they have come to America to escape persecution. This is one of a series of details that emphasizes their lack of control, the sense that the forces of the world are swirling around them with no regard for them. Their situation counterpoints their son's situation. While his 'referential mania' causes him to think that he is the focus of all things, they feel the opposite: that they have lost their connection to the world and its events, to the order and meaning of things. It may be that their son's condition stems from the same feeling--but in order to combat that feeling he has to construct an insane reality. In any case, paragraph three provides us with the details which emphasize the couple's lack of control and connection:
"the underground train lost its life current between two stations. . . . the bus . . . crammed with garrulous high school children [reminiscent of "A Visit to the Museum"] . . . It was raining . . . a nurse they knew, and did not care for . . . he had again attempted to take his life . . . a visit might disturb him . . . things got mislaid or mixed up so easily."
There is a certain playfulness in all of these details. As readers of a short story, we tend to assign added weight and purpose to each detail. It is easy, for instance, to see the train losing its "life current" as related to the son's suicide attempts. We wouldn't make that connection in real life, but as readers of the story (especially VN's story) we, like the son, (though happily, unlike the son) succumb to a kind of referential mania, as we try to distinguish the design that connects all of the story's disparate elements.