Secret Letters

Dora is a proper young English woman who has discovered
something scandalous about her past: Sherlock Holmes
 is her biological father.
When Dora's cousin, Adelaide, seeks out Holmes to help
 her with a blackmail issue, Dora, a budding sleuth herself,
jumps at the chance to travel to the city to meet the great detective.
Upon arrival at Holmes' door, however, Dora finds that
Sherlock Holmes is dead.
She is bereft, but after a few fiery words with Homes' apprentice,
Peter Cartwright, she is able to recover.
Adelaide still needs help and uses the services of another
detective, one that Peter Cartwright has recommended.
Through some unintentional snooping, Dora finds herself
 embroiled in a kidnapping case. She decides to go undercover
 in order to help Peter, but also,
to get to the bottom of Adelaide's predicament - the two cases
are tied together.
Dora uses her skills to piece together the truth behind the mysteries,
but not before putting herself in danger.
She, of course, prevails and solves the case.
She and Peter have a romantic thing that starts up,
 but the author leaves untied ends, perhaps hinting at a sequel?