I just found an entry for death of a Sarah Short which seems to fit .
Philadelphia, Pennsylvania, Death Certificates Index, 1803-1915 about Sarah Short Name: Sarah Short Birth Date: abt 1851 Birth Place: Scotland Death Date: 9 Mar 1911 Death Place: Philadelphia, Philadelphia, Pennsylvania Age at Death: 60 Burial Date: 13 Mar 1911 Burial Place: Philadelphia, Philadelphia Pennsylvania Gender: Female Race: White Residence: Philadelphia, Pennsylvania Marital Status: Widowed Father: James Schofield Father's Birth Place: Scotland Mother: Sarah Scrassley Mother's Birth Place: Scotland FHL Film Number: 1405414
so if this is correct, then, although spelling is off, it looks like her mother was Sarah Crossley and father James Schofield.
So I will now look for a James Schofield in Oshawa - her death shows her father as born Scotland and the Schofield family I found in Oshawa showed them born England - but maybe related somehow as they are in the woollen manufacturing business as well.
I did not find a James Schofieldin Oshawa.It is possible that whoever gave the name of Sarah's father for her death entry got it wrong.
Have you tried looking for Sarah Jane's birth record at scotlandspeople.org to see who is listed as her father?