What does the description of the house tell you about the family and their relationship to nature?

Although we know that the family plays outside in the yard—as images of them throwing a ball, picking flowers, and otherwise engaging in outdoors activities is etched on the wall of the house after the nuclear attack—the family members appear to be divorced from the natural world.
The family relies entirely on the mechanized house to take care of them. Their interactions with "nature" are through the armies of mechanized mice that clean their home and the metal rats and cockroaches that do other clean-up. The mice are made of metal and rubber and live in "burrows" in the walls that dispense them when cleaning needs to be done. These are all, ironically, "animals" that most people wouldn't want in a home.
Although the family goes outside, they don't need to—the mechanized house waters the lawn for them by turning on sprinklers. The house, alert to anything unauthorized, also frightens away any birds that come close, further keeping nature at a distance.
The animals the family does see appear on view screens on the nursery walls and look unlike natural animals: there are "blue lions, pink antelopes, lilac panthers cavorting in crystal substance."
The story implies that the divorce from nature that technology imposes on this society has led this culture to disaster.