as i understand it, etienne is the only omega capable of carrying on the family line atm. while ascending the throne would put a member on house horace ruling the kingdom, the aristocratic house would ultimately end with him and have to adopt. so the head is thinking he needs a way for etienne to bear an heir for the sake of the family bloodline. i think dominant omega is preferred bc their house is known for producing dominant omegas who are good for marrying off to other families and creating political ties perhaps? or maybe bc they have the ability to birth the next generation? idk if im right but thats what i remember + what i guess
Dominant omegas can control normal alphas with their pheremones. It's why the queen is so powerful. So, it allows them leverage over the aristocracy, which typically prefers primarily alpha/omega heirs.
Currently, Etienne is the last in the line that if a dominant with the ability to have children with the gene. (I think the grandfather is ruling out the uncle, since he isn't dominant)

Why the house Herace needs to produce another dominant omega heir? It’s because they don’t know that Etienne is a dominant omega, right? I’m sorry i’m just a little lost.