Teloch asked: If in the event that Ozai found out about the secret love between the FireFoursome, how would he react? Would he care? Would he try to use it to better control his children? Would he try to NTR any of them at any time just to hurt Zuko?
(I won't go into detail about how he felt about Zuko and Azula being with each other, since I'll tackle that on Defending and Analysing Zucest)
I feel like he wouldn't give a shit, at least at first, and just be very surprised that not only did Zuko manage to get three girls to fall in love with him, but also that he managed to get these three specifically. It also probably never occurred to him that Azula could be interested in girls... or in anyone... or in anything besides being his weapon.
He'd eventually try to see if he can use Azula and Zuko's relationship with Mai and Ty Lee to make sure their families will be even more loyal to them (which is to say, to him) and possibly plan a wedding with whichever girl he deems would be a more beneficial match (possibly cutting ties with the other if it creates drama or just keeping her as a mistress/"giving" Azula the rejected one), and he might give Zuko a warning about not making any bastards, or to at least find a way to make convince people that the bastards are not his in case everything goes to shit and they don't get any/enough political benefit from the situation. Zuko would not like the way Ozai talks about the subject at all, since he pretty much ignores the very real connection they all have with each other and essentially treats Mai and Ty Lee as two more pawns in his game, and Azula would be mad and hurt whenever Ozai implied/praised her because he believes she either seduced the three of them of accepted to join their relationship merely as a way to have more control over them.
As for trying to hurt Zuko, I don't think he'd try to Mai and/or Ty Lee from him, but I can see him trying to make Zuko believe that maybe they're just using him and they would have never so much as looked at him if he wasn't the Fire Lord's son.