Now, now, she was never his mistress. He would have liked her to be, but she refused. She only stayed with the family because she felt she was having a good influence on his questionable character.

The word "mistress" was of course used in the strictly Victorian sense :)

So what was the strictly Victorian sense? If you mean mistress as in "Master and mistress", then his mistress would have been his wife.

As in any woman besides one's own wife that one has any kind of a more than casual relationship with (not necessarily sexual).