Is the priority in purchasing a disputed shop for the heir of the first man who owns the rest of the house and wishes to incorporate it, or for the daughter who benefited from it and conducted business there, knowing that she owns other shops? And does the hadith, "The neighbor has more right to his immediate proximity," apply to this case?

There is no objection to the heirs agreeing on the division of the property, and it is not obligatory to document it. The daughter has a greater right to the shop because she is a partner and wants to buy it, and it is not permissible for her two sisters to sell their share in it to anyone else, due to the Prophet (peace be upon him) saying: "He ruled with preemption in every partnership that has not been divided, or a wall. It is not permissible for him to sell until he informs his partner. If he wishes, he can take it, and if he wishes, he can leave it. If he sells it without informing him, he has a greater right to it." As for the non-partner neighbor, he has the right of preemption over an outsider who is not a neighbor like him. So, preemption here belongs to the daughter.