In ancient times the king in fact didn't hole the most power it was in fact the officials in the court that did. Often the king yes had his queen but the very fact is that his father likely had concubines and consorts that had kids that came from these court servants. So this king as well likely has cousins & step brothers that are all truly holding the power in the nation. We in fact see this in not only Japan, but in Korea and China as well. So yes a set time was given to the king for how many days he was allowed to have with the queen and this was in fact chosen and influenced by the court officials as well. The king was often a seat of yes power but the court officials wielded that power thru the king. The king as well couldn't just force an official to step down as each official held the land of the king in his hands thus a lord of the land and this lord if he didn't want to do something could force the kings hand. Today's emperor of Japan is just a figurehead that wields really no power today after WWII. If you look up the Kim family in Korea you have more detailed information about how corrupt officials bound the monarchs.
the reason for the "rules" and her being a hostage are shaky at best. i know that romance stories don't have the best worldbuilding but come on. he's the king, be can make his own decisions about his queen. and it's not an absolute rule that the king and queen of amaha cannot have a "real" relationship, it's just bc the resentment towards amaha festered and the past king despised their queen. he's not the past kings, he's his own person. the onyl rule in their union is that she's the queen and not only a priestess, nothing else has been notorized to limit them.
one "bc i said so" from the king and there would be no obstacle