The game has established two scenarios in the lore for this type of behaviour: honoured guest and might makes right.
In the first, a high-ranking, well respected acquaintance can be afforded certain household pleasures. With might makes right, it is basically..to the victor go the spoils. Neither one of these two scenarios is in line with the originally proposed Omar storyline. Essentially, the MC would have to give up his high status if he were to fall to such a basic blackmail plot. If he loses the ability to dictate when and how his villa/harem acts, then he is no longer at the top.
Omar is Rabiah's husband, so if you want the husbands to swap wives then he is rather important in your scenario. I don't think we have been introduced to any other married sisters in game so if that is your kink, you have limited options.