Is it obligatory to shorten the prayer or complete it when residing in the town of one's ancestors and paternal uncles, where one owns property and stays for two months or during occasions, knowing that one shortens the prayer in the town of the mother's family, where one owns no property and stays for only two days?

The correct view is that the prayer should be performed in full in the area of your property, your uncles', your grandfathers', and their children's properties, even if the stay is less than four days, because it is considered your second home, and most likely your stay there will exceed four days. As for visiting the area of the maternal relatives, where you own no property, it is permissible to shorten the prayer if you do not intend to stay for four days or more, provided that the distance between the capital and this area is a distance that permits shortening (83 km or more).