Hi I think Mary Swallow and Mary Jackson are the same person. I have found a birth for Mary Jackson 1857 Doncaster, mother Jackson. Elizabeth Jackson is living with Jonathan Swallow, calling herself Swallow, I can find no marriage. This is Mary's mother.
That is a brilliant bit of research.
Given what has been found I see no reason to doubt that Mary JACKSON is Mary SWALLOW.
Whether or not she is Jonathan SWALLOW's daughter might never be proveable.
Philip