The Chronicles of Barsetshire, Book 3: Dr. Thorne

Mary Thorne, orphaned (and illegitimate) niece of Dr. Thorne, has long been a favorite at Greshamsbury House--until Lady Arabella Gresham learns that her only son Frank is in love with Mary. The unhappy Mary is banished forthwith, because the Gresham family fortunes are so depleted that Frank must marry money.

Frank, however, is one of the few completely honorable young men in Trollope's novels and remains stubbornly true to his love. Well, he does propose to another woman, at the insistence of his mother, but only with the virtual certainty that he will be rejected--as indeed he is. The lady is Miss Dunstable, one of Trollope's most delightful characters, a fabulously wealthy thirtyish heiress of an ointment company. She is a bold, witty woman, not beautiful, but attractive in her way, whose wealth invites countless proposals.
After the rather complicated plot unfolds, the tables are completely turned, and Mary is eagerly welcomed by Lady Arabella (who, of course, has always loved her) as the savior of the family.