Is the point of this story that we should prevent technology or is it just about parent-child relationships?
It may seem counterintuitive, but I don’t think the story really is about technology at all. Instead, the automated home, including the nursery, is a kind of placeholder, or substitute, for what is really missing in the Hadleys' lives, which I suppose we could call “love” or “connection.” The parents confuse indulgence with love; their children, are, quite literally, “spoiled” by the comforts of their automatic house—“spoiled” for any attempt by the parents to reconnect (this is why the idea of turning the house “off” for awhile is so repellent to the children). Of course, the problem with the parents is that they have no real clue about what is going on with their children, or how their labor-free house has become more than just a privilege or convenience.
For the children, the nursery is a way for them to explore their innermost desires, and, ultimately, a way to express those desires, a kind of window onto the subconscious, a place where dreams (literally) come true. It’s telling that the parents can’t understand why the children are so interested in Africa—for them, it is just a program, and the solution is to change the channel. But for the kids, the Africa simulation is an embodiment of their anger at being uncared for by their parents, and an expression of how they have turned the technology into a kind of surrogate parent. In other words, they have done exactly what Lydia most fears: the children have “gotten into the machinery” and hacked the nursery. It is not clear whether the children are directly responsible for the deaths of the parents; it may be that the nursery is embracing its role as parent, and is simply being protective. At any rate, it turns out Peter really did mean it when he said he wished his parents were dead!
The story does not suggest that we should prevent technology, but that we should not let it control us; we should not rely on technology to replace our human relationships such as between parents and their children. In this story, the children's humanity is destroyed as their parents are destroyed by the technology in the room, they are cold and have no remorse or regret; they are as cold as the technology that controls the room.