Are there any details regarding what a dying person sees in their final moments, such as seeing their deceased relatives, and what is the significance of her grandmother calling out to her mother while she was dying?

First: There is no evidence in the Qur'an or Sunnah (definition) to suggest that a dying person sees their relatives or other people at the moment of death. Rather, the utmost that has been reported is an account from Yazid ibn Shajarah and Mujahid regarding the dying person's companions appearing to them. If a dying person does speak with their relatives, that may be an illusion and not a real encounter.

Second: Angels give glad tidings to the believer at the time of death, as Allah Almighty said: (Indeed, those who say, "Our Lord is Allah," and then remain steadfast—the angels will descend upon them, [saying], "Do not fear and do not grieve but receive good tidings of Paradise, which you were promised.") The dying person may see them and speak in a way that indicates this.

Third: Satan may appear to the dying person at the moment of death.