Basically, the more they do it, the more the Duke starts getting obsessed with her, while she's getting more and more comfortable with the idea of the divorce being confirmed.
The whole duchy knows they'll divorce and they are very weirded out by the Duke constantly asking for people to keep an eye on her. The duchess keeps confirming that they're divorced, but he keeps going "it hasn't been approved yet!".
Eventually something happens and she gets suspicious, so she asks the madame, who hints that she should check who's under the mask. She devises a plan to do it and discovers everything. She decides to take revenge, in a different way, then disappears right after. By then the Duke is boiled, baked and fried and starts looking for her like a madman.
A few things happen, including him literally begging her for forgiveness, while grovelling on his knees. They make up and get married again, but as a real couple.