In this story, the stepmother isn’t wicked, she’s just stupid and pretentious. And calculating. She has a daughter and a step-daughter and is constantly working out who would be the best (financial and social) match for the two eligible young women. At this point, she’s got wind of the possibility that her step-daughter might attract someone ‘important’.
‘Bashaw’ is an alternative spelling of ‘pasha’, generally referring to a high-ranking official, admiral or general. ‘Three-tailed’ refers to the number of horse tails tied to the officer’s standard, something like the stars or stripes slapped on latter day uniforms, with three being the best you could hope for.
‘It is a very fine thing to be mother-in-law to a very magnificent three-tailed bashaw.’
Source: Elizabeth Gaskell, Wives and Daughters (London: Penguin Classics, 1986 (1866)), p. 340