Lady Like by Mackenzi Lee

Two women, one refined and one ribald, set their sights on marrying the same duke, but instead of becoming enemies, they find themselves falling in love—though not with him.

Harriet Lockhart never planned to marry. She has spent her life defying expectations, playing male roles on London's seediest stages, and doing whatever she pleases. When Harry is contacted by her hitherto anonymous father, she finds herself at risk of losing the trust fund that’s subsidized her lifestyle—unless she begins to lead a more respectable life, starting with finding a husband. 

Emily Sergeant, the picture of modesty, has only ever wanted to marry. And were it not for one mistake in her youth that rendered her a social pariah, she would be appropriately betrothed. Instead, she’s due to wed the only willing—and most abominable—man in her small town. Desperate for an alternative, Emily flees to London to snag a less lecherous fiancé.

Worlds collide, dramatically and hilariously, when both women decide on the very same duke as their best possible chance at a tolerable husband and a secure future. A tongue-in-cheek romp through London's summer season, from balls to brothels, horseraces to duels, Harry and Emily compete for the duke's favor, only to find their true hearts' desires may be more compatible than they ever could have predicted.