@AgentKuga
The prince-regent's plot was essentially to put Rovel in an impossible position where he'd have to somehow "sacrifice" his daughter to protect the integrity and position of his family. He would do this by pointing out via rumour that Rovel's sister-in-law (correctly) was being unfaithful (to some degree, albeit not physically) to his brother, isolating the family socially and thus weakening them. The problem is that it's not a baseless rumour because everyone at the wedding clearly saw her rubbernecking at Rovel, but no one in their right mind in a feudal society would've dared spread a rumour (even a correct one) about a Ducal family since they're pretty much one step removed from the Crown. So what did the prince-regent do? He had his mother, the Queen (the only other person of sufficient social rank to actually be superior to a Ducal family) spread the rumour instead. Based on what I saw, the prince-regent's plot was then to offer to help dismiss the rumours in exchange for, I imagine, some kind of custody or betrothal for Ellen that would bind her to the Royal Family (who are desperate to overcome the curse of the spirits).
Except Ellen royally screwed his plot over by 1) her mother hiding away Aria's thorn punishment tattoo on her wrist; and 2) having her openly mingle with servants and other people with her sleeves up, meaning that they could be used as witnesses that the rumour is baseless. So now the one who's screwed is the prince-regent: he could, as he offered, help them dismiss the rumours, but given that high society is hardly made up of morons, everyone would realise that this would mean the Queen (and by association, the rest of the Royal Family) were responsible for spreading what they presume to be a baseless rumour. And since Rovel and Ellen now hold the witness testimonies of the servants and other people in their hands, and Ellen deduced the source of the rumour, they can always come after him at any point in the future with that discrediting fact. This, in combination with the previous King's mishandling of the Agielle situation, would be cripplingly discrediting for the Royal Family (and in a feudal society, that's very, very bad).
So, essentially, Ellen placed the prince-regent in checkmate, robbing him of any leverage over Rovel's family.