«Obedient Bride» by Mary Balogh

Geoffrey, the new Viscount Astor, needs a wife. Since he sets no great store by love and romance, he decides it would be eminently sensible to offer marriage to one of the three daughters of his predecessor. He has never met any of them and has no preference. He leaves the choice to them and their mother.
Arabella, the middle daughter, volunteers to make the sacrifice and marry the earl since her older, far more lovely, sister is already in love with someone else. She prays that he will be an older man of few attractions, for she sees herself as plain and uninteresting. She is dismayed to discover that Geoffrey is, in fact, young, handsome, and fashionable. She vows to be a dutiful, obedient wife and to devote her life to making him comfortable.
Arabella's plan seems to be working nicely for both Geoffrey and herself—until, that is, she discovers something about him that shocks her to the core. It is an offense she considers quite unforgivable. And when Arabella makes up her mind about something, she is not easily persuaded to change it.
Geoffrey is finally shaken out of his complacency to the discovery that his wife means far more to him than he had realized. But how is he to win her back when she flatly refuses to be wheedled out of her outrage?