The whole metaphor of "I Stand Here Ironing" is that a time proven, methodical, contemplative process for managing an unruly material object is compared to managing a young person's life that has become unruly. The metaphor is implemented through the time proven method of ironing, which manages unruly fabric by removing wrinkles and putting in desired creases, such as pleats. In order for this story to be relocated effectively in another place and time, another such contemplative, methodical process for managing the unruly would have to substitute for ironing.
It is conceivable that the story could be relocated to a sheep farm, maybe in Australia or New Zealand, and sheep shearing could be substituted for ironing. At certain times of the spring, which varies per sheep breed, the wool of the sheep separates from the body of the sheep of its own accord and can be harvested simply by lifting it off. This is a time proven, methodical, contemplative process for managing something that has become unruly. It would serve for a story like "I Stand Here Ironing" in which a parent contemplates whether a school authority figure is correct in suggesting that a young person is unruly and in need of managing like the wool on a sheep or the wrinkles and lost pleats of a dress.
Moving the story to a technological time and place seems a little more difficult. Perhaps the long process (at least to the novice) of activation of and transferring data from a existing mobile phone to a new replacement mobile phone could substitute for ironing; it might be set in some home office or study space. The process may not be time proven but it is a long process that may lend itself to contemplation and is methodical and may be seen as a process that manages something unruly.