The Duke Who Came To Town by Sophie Barnes is Book Three in "The Honorable Scoundrels". This the story Josephine Potter and Devon, the Duke of Snowdon. I have read (and loved) the other books in this series but think this can be a standalone book.
Josephine is the older sister who has to take care of her sisters. Doing so has brought her to being an account for a hotel. When she is let go she argues with Devon who has insisted that she should be work as she is the granddaughter of a Viscount.
I loved watching their story play out and just added to my love of this series.