It is impossible to go back and understand what was going through your grandmothers head at that time.
It sounds like your mother rejected her parents more than they rejected her.
It was a difficult time and was not helped by the various groups who pushed an assimilated lifestyle on the Jews of that time.This caused even more of the situations you described with your great grandmother and more problems.
Obviously, a child brought up in warm and excitin Jewish house will not seek to go away from this, so perhaps here, was the real source of the problem.
In the old days, people just "grew up" in a shtetl environment.People being people grew lazy, and one didn't grow up with reasons why they are doing things, you just "did" them.Some groups, such as Chabad, instilled in children "why", but even here, the "why", was usually instilled at a later age.Others never learned the why, and subsequently, when they had a chance to do something else and didn't feel beholden to being Jewish, so they chose that!
Perhaps I am oversimplifying many forces, but it is only recently in America, since the last world war, that it has become popular, thanks to Lubavitch, to explain carefully to a child "why" we do things and to make an effort to see that children get a proper education.
In the old country, there simply wasn't money, so girls learned from their mothers.
The problem with this system, is that the first to fall prey to the proponants of assimilation, were unfortunately the women and children.
Now-a-days, things are different, and a person has many choices of how to educate a child.There are, thank G-d, many yeshivos and seminaries for the girls.
In those days, when a person live literally, "hand-to-mouth" (Thank G-d, we cannot even imagine such a life), so if you have a choice to eat or educate your child, it was a difficult descision.Boys, usually got cheder education.Girls got a more informal education, but they were usually quite knowledgeable from a "working experience" of Jewish Law, while the boys learned the theory, they might never actually use it until they got married, while the girl would live it and use it daily!
And she could be relied upon, as the girls of that era were solid in what they knew!
Still, it was a very impovershed period.
The Jews were forced to live under laws that didn't allow them to work in normal jobs.
As farmers, they were pushed onto certain areas of land that were not as fruitful as normal farmland.
The Czar was constantly kidnapping children for his army and keeping them for 25 years.
Pogroms were a constant fear.
This was the life that a Jew lived in those days.
I will point out that the popular film version of "Fiddler on the roof" was predated by an old silent version, which is about 4 hours long!!My grandparents once took me to see it and thank G-d it had subtitles in English.
This original version had the daughter run off with the non-Jew.Of course in those days, we knew what the non-Jewish Russian peasant was about.He was a drunkard, who would beat her silly!In the end, she, being the smart Jewish girl she was brought up to be, ran away from "Mr. Handsome, but drunk and a wife-beater" and ran back to the loving arms of her family!!!
The American 1960's version would like to imagine that the Russian Peasants of that era were not this way, and try to rewrite history.
But, truth is truth.
Even, the assimilated film-making Jews of the 1920's knew what Non-Jew was about.
Now, on the subject of runaways, etc.
It was not uncommon (nor is it still uncommon today) for Jewish families to "sit shiva" for a child who marries out.
This is for the traditional family.
I remember a story once about a black nurse whom someone once approached in the Psych ward of a hospital.
What happened?A rabbi, Rabbi Mentlik A"H had been put in this hospital and they were short of beds.So they stuck him in this floor.The nurses there do not pay special attention to their patients due to the nature of the place, and so, one of the students there, protested to the head nurse about his poor care.It turned out, that she had been the nurse who took care of the Lubavitcher Rebbe when he had a heart attack.
So, the student was curious what the Rebbe would have to say to a Non-Jew.So, he found out the Rebbe spoke to her in Yiddish!!
And she asked the Rebbe, what does "Shiva" mean?
So the Rebbe told her, Shiva means that a family sits for seven days (from the word "Sheva" meaning seven) and mourns for a dead relative.
She told the Rebbe that her mothers family had sat shiva when her mother ran off with her mother.
A Jew is after all, someone who is born from a Jewish mother or Converts by going to a Bais Din (A Rabbinical Court).
You have a fascinating story.
Is this your mothers, mothers, mothers mother?
If so, this means you too, are a Jew!
Wishing you well,