Originally published in a weekly magazine in the late 1800s, this prose foretells the fate of an individual according to when they were born. More recently it has been modified and used in a television adaptation of a famous animated film. What is the prose and how was it used in the adaptation?

Monday's Child

While recent generations have grown up with the version which in which "Wednesday's child is full of woe" an early incarnation of this rhyme appeared in a multi-part fictional story in a chapter appearing in
Harper's Weekly on September 17th, 1887. In that version "Friday's child is full of woe." In addition to Wednesday's and Friday's children's role reversal, the fates of Thursday's and Saturday's children was also exchanged and Sunday's child is "happy and wise" instead of "blithe and good":

This poem was recited on Snow White, starring Kristin Kreuk, to describe the new names of the dwarves.

https://en.wikipedia.org/wiki/Monday%27s_Child