Sara,
Andy has some good suggestions.
It might also be worthwhile to try to find a baptismal record for Mary in case it gives any clues about Ellen. You could check the records forward for any other children of the same mother (it would be helpful if you first checked for a later possible marriage date and location for Ellen).
I would be wary of relying on information from Mary's marriage certificate (if she married). If she was illegitimate, she might have made up a father's name, and that would only confuse matters. Just something to keep in mind. One of my husband's ancestors was illegitimate. Her stepfather's name was given as her father's with her own surname appended to his. Luckily, I was able to track them in the census and figure it out (with the help of a Rootschatter).
If Mary was born in a hospital for unwed mothers or if she was given up for adoption, you could find out if the place has kept its records and if/how you can access them.
The local library, archives or family history society might be a good place to inquire. They might have marriage and/or death indexes for the area that they could check for you. They could also tell you what other resources are available (school records, for example).
Regards,
Josephine
