I don't think her mother would come into it - it's not at all likely the parents are still together, as they were not married. The mother may be dead, since otherwise the father (who does at least take responsibility for his little mistake) would be more likely to have left the child with her and supported both in some quiet place, perhaps sending Harrriet to a day school when she was old enough. He is not poor - Harriet has always had a good allowance as well as Mrs Goddard's fees. Only Emma is (or was) convinced he must be a gentleman - he might or might not be, but as you say it does not matter, because whatever he is he does not appear to want to acknowledge Harriet or introduce her to his associates and friends, whoever they may be. He might give her a modest dowry if she marries, as it would signal the end of his responsibility for her. I think it quite likely that he is, and possibly was before Harriet's birth, married to someone who is not Harriet's mother.