How does this story depict "The Cult of True Womanhood"? How does it show the virtues of woman back then?
Well, this story does a good job of critiquing some elements of the cult of true womanhood, but actually, it doesn't fully focus there. By that I mean, the narrator's willingness to live for her daughter and to spend her life doing domestic chores fits, and shows that both of these are fairly dead end ideals. The narrator seems stunted and unhappy, but not very aware of either. It also shows, in the daughter's wild actions, that this "cult" is passing—that some women find other ways to be happy, even if they aren't the healthiest way.
However, because the husband/father left the family, this is partially not a discussion of that set of values. Yes, you could read this as an attack/critique of those values, since the man leaving left them so vulnerable, but mostly, this was already one possibility in the period, and the man was seen as unworthy for abandoning them.
One of the keys to understanding this passage is to focus on the balance between the mother's willingness to have devoted her life to her daughter, but also her concern that her daughter find her own way while also not ending up with the mother's fate. The mother sees the potential her daughter has and fears the daughter will not reach it, yet she also understands the burden of being a woman, and she knows her daughter potentially faces the same challenges as she matures.