Part of the success of this excellent poem lies in the allusion that it contains to the fairy tale of Snow White and the Seven Dwarves and how the evil stepmother used to look into her magic mirror every day and ask the fatal question: "Mirror mirror on the wall who is the fairest of them all?" Thus, the reference in this poem to the speaker's children looking into the "mirror mirror" is a reference to this fairy tale and the kind of unhealthy focus on beauty and attaining it that it indicates. Note how the allusion first appears in the first stanza:
...peers into the mirror, mirror on the wall
frowns at her face, her eyes, her skin,
The answer to the unspoke question is obviously found in the "frown" of both the daughter and the son as they find that they do not measure up to society's expectations or standards of beauty.