[General] writing her name in the perfect script, 'her teacher an ex-nun' [...]

[suprunp]

She smiled, amused and faintly dismissive, gesturing to the robe on his arm.
"For your wife?" she asked.
She spoke with what he recognized as a genteel Kentucky accent, in this city of old money where such distinctions mattered.
[...]
She agreed to see him again, writing her name and phone number in the perfect script she'd been taught in third grade, her teacher an ex-nun who had engraved the rules of penmanship in her small charges.

(The Memory Keeper's Daughter, Kim Edwards)

These both sentences seem to be of a similar style, that is when second part seems to be slightly 'estranged' from the first part, nevertheless, the former is strongly tied to the latter (it is my own description of what I feel when I read these sentences).

What does this style signify? What does author want to emphasize by using this style?

Thanks.

 

[Ouisch]

Actually, the sentence parts aren't that "estranged" if one is familiar with US culture, especially that of the American South.

She smiled, amused and faintly dismissive, gesturing to the robe on his arm.
"For your wife?" she asked.
She spoke with what he recognized as a genteel Kentucky accent, in this city of old money where such distinctions mattered.
[...]

If you've ever been to Kentucky, you would note that there are a variety of accents. Some of the more aristocratic families (that is, those wealthy, well-educated families) tend to discriminate against those who speak with a "hillbilly" accent. And "old money" carries a certain prestige - much like Britian's Royal Family, "old money" families in the South have owned land in the area for over a century and became wealthy back in the 18th century, whether from cotton farming or banking or raising thoroughbred horses or whatever.

She agreed to see him again, writing her name and phone number in the perfect script she'd been taught in third grade, her teacher an ex-nun who had engraved the rules of penmanship in her small charges.

It is an historical stereotype (somewhat based in fact) that nuns who taught in parochial schools were particularly strict with their pupils. Each student's handwriting had to conform to the samples in the penmanship textbooks, and left-handed students often were forced to learn to write with their right hands for the sake of conformity. Unlike public schools, parochial schools charged tuition, so only families who could afford it sent their children there. Thus at one time a parochial education was a mark of economic aristocracy, and anyone who'd been educated by nuns had very precise handwriting and impeccable manners. Some teaching nuns eventually left the convent but still brought their strict practices with them when they taught in public schools.