Delayed, but still wanted to post a thought here to see if my thinking comes true in later chapters:
Nina is a child of the current king's father, hence the red eyes, and someone like the saintess, hence the blonde hair. The children on the old king's affairs were sent as far away from the capital as possible so there was no chance for them to come running for the crown. This would also explain why her 'holy powers' don't clash with the current king's; they have some of the same blood running through their veins.