Well, falling in love is not really something that easy now is it? If it's something that's said as a curse in the family, wouldn't you just avoid it all the more? Just because they have sex, doesn't mean there's love? Also it's the princes and kings that needs to fall in love for the curse to activate, so the other party can fall in love all they want, nothing will happen.
The crown prince is (supposed) emotionless, I mean, he even tried to kill that guy on the spot until Collin told him not to traumatized the new sister. And from the prologue, all the 3 brothers are especially surrounded by scary rumors that made them sound heartless.
There's probably a gay prince/king somewhere in the bloodline, but so long as they didn't fall in love. It's a curse. They gonna try very hard not to fall in love regardless of sexual orientation.
The concubine was sent away before she gave birth so they couldn't know if it's a boy or a girl. I don't think the curse being broken is something announced like "ding" it's broken so they didn't know. Also since at that moment it was chaotic due to political struggle, they didn't know where the concubine ended up. I'm sure that will be revealed in the future plot.
I have two concerns my first one is if they don’t have maids because of the curse because of the accidentally fall in love with any of them the maids are going to try to kill one of them or if they have their child they might love their child and their child’s gonna kill them but what happens when one of them is born gay like dude gonna die immediately it must’ve happened at least once
but that also makes sense to why they wanted to keep the concubine the mother of the princess away because the king actually loved her
Number two concern wait how old is The princess because that means they should’ve known immediately because it’s just her birth because everybody keeps implying it’s just the birth of a girl meaning that the curse has already been broken for a long ass while so wouldn’t they have already known immediately the oh wait the curse is broken or is it that they have to know of her existence and bring her into the castle for it to be broken because it makes no sense that they wouldn’t know if the state of the cursed at Philly the whole entire imperial family in the minute that it’s broken they don’t know like to certain extent yeah you guys are around men all the time but I’m pretty sure One of you has wanted to get freaky or some random person that doesn’t know you guys of gotten obsessed with you and has accidentally tried to kill you and when the person to forward their love to you they didn’t kill you and that didn’t seem weird