A mortal curiosity / Ann Granger.

Enhanced descriptions from Syndetics:

It's 1864 and Lizzie Martin is leaving London for the south coast of England to be the companion of Lucy Craven, a teenager who lives in seclusion with her aunts and has recently lost an infant daughter to illness. En route, Lizzie meets Doctor Lefebre, a slightly off-putting gentleman headed for the same destination. Lefebre, it turns out, is an alienist hired by Lucy's family to determine whether the young woman is mad. And he discloses something shocking: Lucy Craven doesn't believe her daughter is dead; she insists the baby was stolen from her.

In Hampshire, complications mount. Late at night, Lizzie hears furtive voices outside, there's a gentleman farmer whose demeanor with Lucy seems unusually familiar, and, while Lucy proves a bit moody, she hardly seems deranged. The girl's aunts are clearly withholding something. . . . These tensions come to a head when a man is found dead in the garden, stabbed with a knife from the aunts' home.

Lizzie calls upon her beau, Inspector Benjamin Ross. Together, they find themselves entangled in a mystery as bewildering as any they've faced.