Two different kingdoms or haven't you read the other two books ....
No this person is right, it says it on this page: http://www.mangago.me/read-manga/ousama_game_takagi_ryo/tr/28940/page/39/
So the 4th prince is actually Ryuuga. Don't know why the author changes the 4th prince to Rien but whatever.
Because the 2nd one was disowned or something like that
Isn't the fourth prince that really lecherous Ryuuga? Who the hell is Rien?