Why is Dorne culturally so different from the rest of Westeros?

Question

We know that Dorne is part of Westeros like other regions. How come it is so different from them culturally? There is difference in other kingdoms, too, like Northern people respect the Night's Watch and give value to pride and honour. Southern people are relatively different. But those are minor differences. But Dorne is a totally different case, they are different in major things like:

1. They give equal right to daughters for inheritance like sons, whoever is elder.
2. They have Princes instead of Lords or Liege Lords.
3. They publicly acknowledge their mistress (call them Paramours) and bastards.
4. Bisexuality of Prince Oberyn also seems to be acceptable wherever it will be a religious scandal in other regions.

Answer 1

Geography

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.

Cultural

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.

Political

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.

Answer 2

Dorne's differences have to do with its vastly different history from the rest of Westeros, due in part to its geography.

Its Game of Thrones Wiki entry provides a short overview, but you won't get the full picture until you read The World of Ice & Fire : the Untold History of Westeros and the Game of Thrones by George R.R. Martin, Elio Garcia, and Linda Antonsson.