Its established that the previous king had love for soo won but some reason didn't want soo won to go in king hiryuu shrine and didn't want his daughter to marry her.
Soo won says he killed his father which i dont know i believe but on the outside people know him as a pacifist king.
Also it seems both yonas dad and mom knew she would be the reincarnation of king hiryuu. And for whatever reason the previous king before that chose yonas dad over soo wons dad as next successor.
What if king hiryuu from his shrine is letting them know his will and knew they wouldn't be fit to rule.
Soo wons dad could of acted in public as he accepted it and privately tried to take the throne. We know soo wons dad is a brutal guy and soo won is much more benevolent but also would rule with iron fist if he felt necessary. Not saying he's a bad guy but sometimes his decision making is too cold and calculating. His rulership is largely based on force and deceit.