Yes, your Great Grandparents, William and Jane are the right ones, Market Gardeners at Dunston. Father went there to meet the family (I think I may have the address somewhere in his papers)
Now, what I believe happened is this (although Eliza was known to tell lies and embellish!!!) Eliza Hartshorn was born around 1870 in Shrewsbury. In 1887 she went to the Workhouse at Atcham to give birth to my Grandfather, John Wiliam Hartshorn. She then went to Newcastle to find William Kennedy who was a market gardener, only to find that he had got another girlfriend and, in fact, had just married her. In 1898, John William was placed in the Industrial School, Newcastle and Eliza moved around before moving to Leicestershire. Granddad was given a training in printing and went on to become a printer which was his trade. He also moved, on leaving the Industrial School, down to Leicestershire where he met my Grandmother, Margaret Wood. They had one child, my father Stanley. There was no knowledge of or contact between them and the Kennedys until we started to research our family name. It was only on what Sarah Jane told father AND the remarkable likeness to my Granddad which convinced my father that the Kennedys were indeed our "family". And that is really all I know. If you had any rumours or anecdotes concerning William and Eliza's "goings on" I would love to hear them. Or a photo?
Regards,
David