Is this gift that the grandmother bestowed upon her daughter (the questioner's mother) permissible in Islamic law, knowing that the grandmother is still alive, that she gifted it in full health and of her own free will, and that she refused for the mother to distribute it among her sisters?

Parents must be just among their children in giving, unless there is a legitimate reason for preference, such as need, illness, a large family, or if the giving is related to the son's wickedness or innovation. Preference is also permissible if the children agree to it, as in the story of Aisha, may Allah be pleased with her, with her father Abu Bakr, and the story of Asim with Umar, may Allah be pleased with them both. There is no harm for the mother in accepting the gift, and she should act wisely in distributing the land to avoid offending her mother. She can postpone the distribution or distribute it without her mother's knowledge, and she must explain to her mother the obligation of justice among children.