Debt of Dishonor by Lillian Marek

Kate Russell is furious.

It was bad enough that her father had let her grow up in virtual poverty, but now her dissolute brother wants to use her as payment for his debts. She runs away, determined to make her way so that she will never again be at the mercy of powerful men.
Then she encounters the Duke of Ashleigh.
He has overcome the shame of his parents’ scandalous lives and has a well-deserved reputation for honorable behavior. Then he encounters Kate, the niece of an old friend. There is some mystery about her background.
She is not the sort of well-bred lady of impeccable reputation that he plans to marry someday, but he can’t get her out of his mind.