Kim Jong Il's forth mistress, Kim Oak try to put third son, Jung Woon as next heir of N.Korea.
Kim Oak's biggest rival would be the oldest son, Kim Jung Nam therefore she is using her power to check Jung Nam's division as well.
The Reason Kim Oak is supporting the youngest son, Jung Woon is because of her power sharing in the future. Since Kim Oak and Jung Nam has not much of age difference that Kim Oak may lose her power becuase of Kim Jung Nam's charismatic character. Therefore Kim Oak is secretly supporting Jung Woon as next heir of N.Korea.
Right now, Kim Oak's position in N.Korea is huge that she is taking care of most of Kim Jong Il's work. So there is some possibility that Jung Woon would be the next heir.