Hello! The grandmother and granddaughter in this short story are nameless; we only know the name of the grandmother's daughter, Sylvie. The story makes it obvious that both the grandmother and granddaughter do not get along. We soon find out why: the grandmother had Sylvie out of wedlock and had a hard time accepting Sylvie.
...the swaddled package meaning no more to her than an extra anything, something store-bought, something she could take back for a refund.
The grandmother knows that Sylvie came to be from a union of lust - 'there was no love in the begetting.' Before Sylvie dies, she gives birth to a daughter that the grandmother thinks is just like her, who 'would carry the hurting on into another generation.' The grandmother and granddaughter live together with their dog. When she finds her granddaughter with her arms around a man on a bike, the grandmother is unapologetic in her demand:
"She's underage." Just that. And put out her claiming hand with an authority that made the girl's arms drop from the man's insolent waist and her legs tremble.
However, both do not bargain for the fact that the men ride back around shooting at them. It is obvious that they are looking to have some fun of a sexual nature, at the expense of the grandmother and granddaughter. The grandmother drives hard and manages to evade the men who are on their motorcycles, but not for long. They eventually make a run for it into the woods and hide under the Greer cottage dock. Both submerge themselves, but the dog makes too much noise. The grandmother is forced to drown the dog for both their sakes. The men eventually go away, but not after some heart-pounding moments.
As to whether either the grandmother or granddaughter is a more sympathetic character, I imagine that choice would depend upon perspective. As a suggestion, you may decide to make your choice based on your own sense of which character you most closely relate to.
The grandmother knows that she will always feel great sadness for the way things have turned out for both her daughter, Sylvie, and her granddaughter. She cannot live in the past; only the power of the present is in her hands. She tells her granddaughter that 'Around here, we bear our own burdens.'
She has resigned herself to the consequences of her choices and seeks to carve out a better future for her granddaughter. She tells her granddaughter that it was she alone who made the choice to sacrifice the dog; she tells her granddaughter not to apologize. In that one heart-breaking act, her resolve to remedy the mistakes of the past has begun to bear fruit. She will earn the trust of her granddaughter, and thus, heal the pain of three generations.The grandmother is the catalyst for change in her own spartan way.
She is lost in more ways than one. Bereft of a mother, she is a sympathetic figure; not even her own father wants her around. The grandmother says that her granddaughter takes after her own mother, who went around with the wrong guys. The granddaughter distrusts her grandmother; all the adults in her life have seemingly let her down. She is angry and bewildered at the turn of events; like her mother and grandmother before her, she looks for love in all the wrong places. Her sexuality has blossomed at fifteen, but she is still a child in her desperate need for love, belonging, and identity. How should a girl her age work out her pain? In the end, she realizes that it is up to her to learn to trust, hard as that may be. When her grandmother saves them both from the motorcyclists, by drowning their beloved dog, she experiences a powerful moment: her grandmother's love and protection becomes the catalyst for her dawning change of heart. For the first time, she also realizes that she is not the only one who has suffered:
The girl walked close behind her... close enough to put her hand forth... and touch her granny's back where the faded voile was clinging damp, the merest gauze between their wounds.
I hope this aids in helping you answer this question. Thanks for asking!