And what is with the "is 4 years old, but looks 7" bit? Why do we need to know that? What effect is that meant to have in the story for us reading it?

I interpreted that to mean the kid looks old enough not to get a pass for blurting out something "rude" the way toddlers and preschoolers can, which is why the mom was so adamant about correcting him instead of letting it go.

Think you nailed it here. She thinks the kid looks old enough that people would think it was her fault for not training her child to play the pronoun game better.