Give my Word by Linda K. Hubalek

Rancher Beckett Brenner was thrilled to change his destination to escort Greta Wilerson to Kentucky instead of continuing on the planned train trip to Texas.
Beckett, his brothers Asher, and Carsten, along with their neighbors, female cousins Greta, Alva, and Emma, were on a trip paid for by their respective grandfathers, to explore the women’s family’s past in Texas’ cattle drive history.
On the first leg of their train trip, Greta read in a newspaper the Kentucky Derby was going to be held that very Saturday, and she was determined to be there in person to watch it. Beckett jumped at the chance to escort Greta, and they left the group to travel on by themselves.
Hilda, Greta’s mother, was a horse trainer first, a wife second, and a mother third. Greta’s upbringing meant she was an excellent horsewoman but also a wild and compulsive tomboy. She wore Beckett’s patience thin before they even arrived at Churchill Downs.
But Beckett and Greta work together when they find a scared horse and two injured people in the horse’s Churchill Downs stable stall.
Instead of falling in love with each other, though, Beckett and Greta find new partners and passions while dodging danger and participating in the race of a lifetime.