He's technically working to break up the marriage, but it's more because he wants instability in the eastern empire, which is militarily on par with his homeland and the western empire, so if a war broke out a combined force of the 2 would win, but it would severely weaken both armies and cause massive slaughter and chaos of civilians, so the best scenario is to either end military issues (not really possible for a few reasons) or weaken the kingdom(this doesn't always mean conquest btw, as it also means trade route control and the opposing nation's mistreatments).
The duke is looking at this pragmatically, navier is far more a better regent than sovietshoe and rashta couldn't lead a parade much less a country, so finding a way to remove her from the empress position while not resorting to violence which would definitely lead to war is in his best interest, while also not pissing off henley who is fond of navier, basically the true power of the royal family is mostly behind navier who keeps things stable between the aristocracy, royalty and commoners as well as handles governmental affairs better, all of this leads to much bigger spoilers so i'll stop explaining this here.