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The Tug owner was John Batey my great great grandfather, and Atkinson, known later as Thomas, was his brother. I don 't know why he changed his name. The name Atkinson came into the family through their mother who was Hannah Brown .  When John was baptised one of his sponsors was called Atkinson Brown but I don't know the exact relationship in the Brown family.  Atkinson did not go direct from N. Shields to S. Shields, I think he was in Hartlepool at one time.  He and his wife and two youngest children went to America  Plymouth PA, in about 1870 I think.  His daughter Robina may have married a man of Welsh descent called Richards
Your George Batey is not an obvious relative, but I have not researched the Willington antecedents yet.  There were certainly Bateys in Willington Quay area well into the 19th century  John and Atkinson I have just remembered had two younger brothers called George.  The first died in infancy but the second George, b. May 1824 I haven't been able to trace in later life.  Could he possibly be your ancestor?