Makes sense but I think the manga kinda has hinted the inevitable love between the king and first queen. Like they literally spend their whole time together since childhood there must be a bond and such... but maybe it's not true or realistic coz they both were confined to only each other and there wasnt much choice for them either. Their whole future was decided by others so they didnt had other experience either.. all in all the first queen is maybe infertile or something happened to her children, she cant give birth. Marrying another wont make any progress.
She's a girl, so she can't inherit the throne. That was implied. Therefore the prince born out of wedlock had to become king, and then marry her for support through royal blood. She wants to thin the "dirty" blood of the maid that have birth to the king through royal blood (her own or that of other royals of their nation).
no matter how many times i read this i cant understand the problem with a heir, the first queen is also apart of the royal bloodline so couldnt she just take the throne with her man of choice and still keep the royal blood alive?