To Pleasure A Duke by Sara Bennett

Eugenie Belmont comes from a disreputable family. Despite her boasts to the Husband Hunters Club, the Duke of Somerton would never want to marry her, and yet that is the task she has set herself. After an unfortunate incident with a goat, things can surely only get better. Eugenie finds herself liking the arrogant duke more and more, especially when he agrees to accept the dares she sets him. And then one of her brothers upsets their budding romance, and Eugenia invites herself along with the duke on a rescue mission.
Sinclair St. John, Duke of Somerton, is all too aware of his consequence. His boyhood dream of being an artist was swiftly brought to an end by his formidable mother, and now he is too important to indulge in romantic whims. Eugenie Belmont seems to bring out the worst in him. Or the best. He even begins to dream of a happier future…until Eugenie’s disreputable brother runs off with Sinclair’s spoiled sister.
But what starts out as a race to save the girl’s reputation turns into a wild and romantic adventure.