The single most crucial part of it was the way her daughter died. In the story, she dies in a (very preventable) climbing accident, to make the point that her mother knew about it and could have just told her not to go (or go a bit later), whereas in the movie she died of cancer, which just completely invalidates the entire point.
In the story this climbing accident is a powerful example.
It is preventable in the case of not knowing the future (yet it this case we have no idea that it will happen). If we are in the state of knowing the future, it is a part of the reality fabric, it IS, just separated by an interval of time.
The single most crucial part of it was the way her daughter died. In the story, she dies in a (very preventable) climbing accident, to make the point that her mother knew about it and could have just told her not to go (or go a bit later), whereas in the movie she died of cancer, which just completely invalidates the entire point.