It seems to me that Elly's "Thou shalt not know" spirit comes from her barely-hidden contempt for children. In her eyes, it's quite clear that children simply scurry about being mindlessly destructive monsters who do irrational things so that they can demonstrate their hatred for order and parental authority. Since a small child doesn't know or care about the things Elly does, having to give up her time and wait for the child to grow up to pursue her alleged interests is a horrible thing. After all, there is the possibility that Elly could spend so much time becoming a part of her children's lives that the university student who wanted to set the world on fire would become a stranger.
Of course the paranoid dread that she'll become a useless housewife and mother is not the only thing keeping Elly from wanting to waste time looking at useless children who don't know anything. We also have to remember that she is very, very bad at multitasking and budgeting her time. She gets so wrapped up in whatever she's doing at one point that any competing priority is simply too much for her one-way brain to handle. Being interrupted is something of a defeat and therefore evil.
Finally, we have to contend with the fact that Elly just isn't very good at understanding risk. The same woman who bawled pathetically because John was trying to scare her with his scary, scary stories about why he needs comprehensive life insurance seems unable to wrap her brain around the possibility that her inattention would lead to a ruinous outcome. Since she seems convinced that her children only move around to spite her, it would seem that she thinks that if she isn't looking at them, they'll do what children are supposed to and sit like grinning little dummies. This belief that the natural state of children is motionlessness is more or less why she said April toppled into the water; since she sincerely believes that children only move when she's looking at them, her mind painted a picture of an inert object sliding into something.