Is it permissible for my husband to prevent my elderly family members from visiting me in my home and seeing their grandchild, given that there is a dispute between them?

You must strive to reconcile your family and your husband, and clarify to him the prohibition of shunning a Muslim for more than three days without a legitimate excuse. Emphasize your family's desire for reconciliation. If the husband insists on his stance, then it is obligatory for you to obey him, and it is not permissible for you to allow your family into his house without his permission, because it is the husband's right that his wife does not permit anyone into his house except those whose entry he approves, whether they are relatives or strangers.