JJ said: "He may have said I 'll marry you, but not keep the children."
My great-aunt probably would have been better off if my gr-grfather had said just that. Instead, she lived with a stepfather who refused to acknowledge her - she never used his surname, she wasn't in the family photos, she didn't get an inheritance - and when they immigrated to Canada as a family, she remained single and worked in a factory all her life -- fortunately, for a model employer, and she was later surrounded by sisters and nieces and nephews, and ultimately me and my cousin before she died, who loved her dearly.
Being a home child wasn't always the worst fate! My grandmother's other sister married a man who came to Canada as an older home child, i.e. as a farm labourer, and they had their own farm and they and their descendants have prospered.
Enough time passed between Mary Ann's birth and mother Sarah's marriage that it is unlikely Mary Ann was John Cowley's child. But Sarah may just have been in a better position to keep a child than she was with her first child.
Remember that not all pregnancies resulted from voluntary activity. My gr-grmother was in service in a household in 1890, and we understand that the "father" of her daughter was the offspring of the head of that household (whose surname my gr-aunt had as a middle name). Young women in that position were very vulnerable to exploitation and abuse, and that could have been what happened to Sarah -- either in her employment or in other circumstances. No support, financial or otherwise, would likely have been forthcoming from whoever fathered her child, in any case.
It's sad to think of the children relinquished to institutions in these cases, but sometimes the situations their mothers were in were just as sad.