
He can blame his THOT mother for choosing the wrong type of man to be the mistress of. The Duke association with the Ephereny name depended entirely on his marriage to the Duchess - its her bloodline. He was from a much lower ranked household - The Hedwigs. For him to have a mistress was an audacious move considering he is basically a consort not the holder of the title.

Whats even better is that before being kicked out by the Duchess, after returning to see her sick son who just died. January is in a good mood (thinking this means her son will be nominated as heir) and pretends to be all "sisterly" to the Duchess who is in deep mourning for her dead son.
The Duchess snaps at her because she can see through January's conniving behavior and starts a catfight she begins to attack the hoe.
whats funny is the maids/servants just stand by as January is getting her assed kicked but the moment she starts pulling the hair of the Duchess they intervene to protect the Duchess. lol

Due to her behavior prior to the Duke's divorce and Rosemond's behavior. Plus the terrible choices she made nobody wants any affiliation with her and that includes her son unfortuantely. She was happy to hear the news that her lover's legitimate son had died - keep in mind the boy was still a child and died a horrific death due to an illness he caught in another country.
It was January he convinced the Duke to send the boy away abroad to somewhere he wasn't suited.
to streets where she belongs. - official spoiler.
After the Duchess divorces her upstart husband when she finds evidence he indeed date-raped her into marriage. She throws out his harlot January along with their bastard despite them having nowhere to go. lol Duchess gives zero fucks.
The former Duke will be sentenced to death due to his affiliation and aiding of Rosemond.
This also means Rosemond is no longer an aristocrat "princess" or marchioness since the Duchess annuls her family's adoption of Rosemond.
Petronilla who remembers how arrogant January was when she lived in the Ducal estate sees the defeated January homeless on the street with her son. Petronilla spares her some change as you would a beggar by throwing it on the ground which causes January to have a scowled look but at the same time since she is now a penniless and homeless wench she takes the money in desperation on the ground.
She belongs to the streets.