Thank you both Gen List Lass and J.J. for your replys and interest in my post.
Gen List Lass : Your thoughts of the children possibly being distant relatives deserves some thought. The thing is the children are listed as being born in England, plus the names Joseph and Emily do not appear to be "Aitken" of "Jamieson" given names in the past. I did a quick search of both Surnames on Bayanne, using Joseph and Emily, and came up with none for Aitken. Under Jamieson there were no Emily's and 18 Joseph's, none of which fit the birth date. Ten of the 18 Joseph's under Jamieson, were born prior to my Joseph, so maybe there is a match there so far as being named after a Jamieson Uncle or Grandfather.
The Lay Preacher I mentioned was my Grandfather, who was a nephew of the Scott, who's line I'm trying to get straight.
J.J. : Yes that is my Scott in the Windermere site and that Thomas Aitkin is my G Grandfather. There are many errors in the Thomas Aitkin info which I forwarded to the owners of the site. Unfortunately the document is static and cannot be changed, but my corrections were accepted to file as information. Their information is pretty much what I started out with about 15 years ago. Perhaps from the same source.
Thanks again to you both.