Dorne is separated from the rest of Westeros by mountains and deserts. That reduces migrations significantly. There are no other barriers like that south of the Wall. Mountains are mostly located at the coasts. It's easier to get to Dorne by ship, but that's not something everyone could afford.
People living in the mountains are described as underdeveloped, like the Hill tribes and the Northern mountain tribes. That could be another reason to avoid mountains.
The Dornishmen are ethnically distinct from the rest of the Seven Kingdoms, being largely descended from Rhoynar refugees who intermarried with the local population of Andals and First Men roughly a thousand years ago. As a result they have very different customs and traditions compared to the other regions of Westeros. (Game Of Thrones Wikia)
Rhoynar came from Essos. Even today the people of Essos seem to be more liberal about sexuality than the Westerosi.
Acknowlediging bastards isn't specific to Dornish, for example Aegon the Unworthy legitimized all his bastard children on death bed. There are other well-known examples of Lords who acknowledge bastards when they don't have any highborn heirs. For example in season 4
Ramsay Snow becomes Ramsay Bolton.
As Dorne is difficult to conquer because of its geography, it was not by war but by marriage united with the Targaryen realm. As a token of goodwill
the Iron Throne allowed the Martells to retain their title [Prince of Dorne] along with their laws. As with most Dornish titles, succession to the title is granted to the eldest surviving heir regardless of gender. (Game Of Thrones Wikia)
The Prince of Dorne has the same function as Lord Paramount in other regions.