The Design of Dukes by Kathleen Ayers

Lady Andromeda Barrington is the most unsuitable young lady in London.
At least in the Duke of Granby’s opinion.
Granby doesn’t care for bastard relatives or tainted pedigrees and Andromeda possesses both. Nor does he like opinionated young ladies who enjoy hurling insults in his direction.

Andromeda is, in short, the most annoying creature he’s ever met.
When she arrives, uninvited, to a house party given at his estate, Granby can’t decide whether to kiss Andromeda senseless or send her packing.
Andromeda is the victim of infatuation and bad luck.
The infatuation is that of her sister for the Earl of Blythe, but the misfortune belongs solely to Andromeda after she is forced to attend a house party hosted by the Duke of Granby. She and the duke are previously, unpleasantly, acquainted. The entire party is bound to be awkward, and their mutual dislike difficult to hide. Her only recourse is to avoid the giant block of ice masquerading as a duke. Thankfully, Granby’s estate is enormous.

But instead of mutual hostility upon arriving, Romy is greeted with unexpected attraction. Insults turn into flirtation. Heated discussions become lingering kisses. Her heart is ruined. Granby may not even have one. And the duke has already chosen another young lady to be his duchess.