Since a seven year old boy cannot raise a child any more than he can was a car, the end result is that a little kid in over his head is held answerable for behavior he can do little to modify; he also ends up resenting the imposition on his free time that he isn't allowed to question. Simply put, Elly's need to do laundry and watch soaps leads her to stand around yowling about why Mike resents Elizabeth so much. She, you see, was made to watch over Phil when she did not want to and she turned out fine so doesn't see her doing the same thing to her own children as being a problem.
She also doesn't understand it when her mother and father pointed out that they only did so because the two of them had to work so as to pay for the university she blew off because there was no naptime. Nothing that we've seen coming out of Jim and Marian's mouths tells me that they have the blindest idea how stupid, stubborn and literal-minded their daughter is so her reasons for having Mike sit for Lizzie when she's there all the time anyway would give them pause. They see a lecturer who hides behind textbooks when quoting annoying tosh; the idea that she thinks the accidental configuration of her home life is a divinely mandated norm would lead to their deaths due to terminal gobsmackage.