Vicki, Frances has raised a good point regarding the surname issue as it is possible the parents weren't married though there's no record of this in the registers. Sarah's mother (or guardian) would have signed a document handing over all responsibility for Sarah to the Home, unfortunately all these documents were destroyed long ago.

There are also the drownings to investigate, if as you say both father and son drowned one would think these tragedies would have been recorded as these would be 'news worthy' events, just like they would be today. I don't know whether it's possible to research historical newspapers online. Could someone please advise?

If you can find evidence of a father and son drowning perhaps this is the important lead you are looking for.