Mail Order Noelle by Kathleen Lawless

He wanted Melanie. Instead, he got Scarlett

Free-thinking, ambitious Noelle looks to move West to improve her newspaper writing career. Wealthy cattle baron, Grant Chisholm, has offered for her sister’s hand, but Merry has other ideas and the girls arrange a switch.
Grant seeks a woman to marry who won’t hamper his lifestyle, but will free him from his grandmother’s matchmaking efforts. His old school mate’s shy, reserved sister seems the ideal choice.
Noelle only needs to get established in the West before she tells Grant he married the wrong sister. Surely a reasonable and wealthy man will annul the marriage and turn her dowry over to her.
Being in Grant’s household provides Noelle interesting research. So does spending time with her husband. Before she can tell him the truth, her sister Merry shows up, and everything falls apart.