What is the ruling of the Sharia on exchanging a plot of land for another larger one, and dividing two adjacent houses horizontally, knowing that the owners of the land and houses are displaced and refuse to discuss the matter, and that there is a necessity to build on this land due to the Israeli occupation?

Your father's cousin is not obligated to exchange his land for your father's land, because he has the right to dispose of his property as he wishes, and based on the hadith (definition): "The property of a Muslim person is not lawful [to take] except with his willing consent." It is not a matter of Sharia (definition) harm for the old house to be separate from the new house, or for houses to be mixed. The Sharia solution for mixing is to adhere to the etiquette of seeking permission or to create a separate entrance for each family. It is not permissible to dispossess your father's cousin of his property. You can try to appease him by offering money or seeking the mediation of good people.