Source To Bite It Off

The Sefer צאינה וראינה authored by R. Yakov b Yitzchok Ashkenazi  - (1550-1624) was geared specifically for women who didn't understand Loshon Hakodesh.
It is a collection of beautiful Midrashim and some Halachos in Yiddish.

Up until  80 years ago it was the most popular Sefer (after Siddur & Tehillim)  Yiddish speaking women possessed.
Illiterate women, organized a "Zogerrin". One who would read the צאינה וראינה   for their group.

In a letter promoting the Bais Yakov Schools, the Chofetz Chaim writes, "the need for
Bais Yakov is also because many women stopped reading  the צאינה וראינה on Shabbos".

The first Mokor (source) where it is mentioned for pregnant women to bite off  from the Esrog is in the צאינה וראינה.

The Mekor Chaim (Bachrach) quotes from the צאינה וראינה to bite off the עוקץ (not the Pitum)
The Mekor Chaim also praises this Minhag.

The Minchas Elozor writes, women should not bite off the Pitum on Hoshana Rabah.

According to Chazal, (.כתובות ס"א) Pregnant women who eat Esrog will have
nice smelling children (no mention of easy childbirth)