Why do you think Annabeth will or will not get along better with her family after her return from the quest?
I think that it will be difficult for Annabeth to get along with her family better after the quest. Annabeth can be cordial and extend a hand to them. Yet, it seems difficult to see her being able to fully integrate herself back with her family. This is because of her own sense of hubris. The sense of pride that she knows better than others is what prevents her from fully accepting much in way of forgiveness and understanding. Part of this comes from the fact that Athena is her mother. Being a demigoddess of Athena, she believes that she is infallible. In her own sense of self is a capacity for self- worship. This makes it unlikely that she will be able to brace for a reconciliation and sense of connection with her family. At the same time, Annabeth has found her place amongst Percy, Grover, and Thalia. To a great extent, they have provided the emotional conditions that she lacked with her own. The tensions that Annabeth experienced in her family makes it unlikely that she would be able to forge a full and complete reconciliation with them.
From an Olympian standpoint, I think that one can see that Annabeth lacks the traits to fully reintegrate herself with her mortal family. Annabeth possesses the intensity and drive of Athena and the Hunters of Artemis. When Thalia suggests that "Annabeth wanted to join the Hunters. Maybe you should think about why," it reflects a spirit of instability that is intrinsic to her. This is not Hestia, goddess of the Hearth. Rather, Annabeth is akin to Artemis in the spirit of the hunt and of the pursuit. This is not conducive to the stable foundation needed to foster domesticity and familial relationships. At the same time, she is of Athena's inventiveness and natural intelligence, which again find more resonance in the hunt and pursuit than in an embedded domestic condition. Annabeth's closeness with Athena would preclude her from being able to develop a sustaining bond with her family, in particular her stepmother. In these ways, I think that a case can be made for Annabeth not being able to fully reintegrate herself with her family. There are attempts in order to make things work, but her spirit will always be outside of the contours of the family.