
The duke and henery(?) are friends and the duke is being a little wingman cause if the empress is still married she can’t be with his friend so befriend rashta to manipulate and her actions which explain why every time he run into the empress he ask her to hit him
Spoiler
He adopts rashta kids the oldest and the youngest after rashta and there father dies

It has nothing to do with reputation, it's about having an heir. Because he thinks Navier is infertile and can't give him any children his only way of getting an heir is through Rashta. So he needs to give Rashta the empress title, thus giving their baby the right to the throne. But he also knows that Rashta is a poopoo brain and won't be able to do a good job as an empress, so his genius plan is to "re-hire" Navier later...

So he find out that’s not this kid and he really divorced the empress over some stupid shit plus the kingdom is going to shit so he try to kill him self but it doesn’t work out he just loses his memory so he finds out again that him and empress aren’t together and she has another mans babies so he goes to their kingdom(in front of her husband) and ask for her back she say no and he offer to be her side piece

So this means just because of his shitty plan, he lost the one whom he loves and now not only he is going to ruin himself but also the empire. We can't call him the emperor. He ain't being an emperor as he is taking things emotionally unlike our empress who was practical and did everything which benefits the empire.
guys correct me if im wrong
the duke want to divorce to the empress, because of that trash??
i think its because umhh you know he dont want to ruined his reputation so he want to be that's trash to be empress because they have a baby? then after 1years he's going to propose to the empress?
i am right or no?