Hi Greg,
Just read your message, and the response-page.
I agree with you that it is strange that, in 1860, Louisa turns up with William and Mary, and the other kids are gone. Maybe the enumerator omitted some of the names in recopying from his work sheet to the official form.
I am not sure I agree that there were two William and Marys, but I guess that's possible. I did a search at the Ancestry site for "William" in Cleveland, born Isle of Man. So I am pretty sure if there was another William Kaighin (or any similar spelling), I would have found him.
I had a look at the 1850 census entry for Louisa at Ancestry.com. Louisa is obviously working to help out her family. No familiar names in this household:
Cleveland 2nd ward #2288: Joseph Marchand 33 merchant France; Delia 33 Massachusetts; Augustine 7/12 Ohio; Elizabeth Benson 20 Scotland; Louisa Kaighn 16 New York.
Have you looked at the Cleveland Necrology File? Lots of Kaighins there.
Start with Cleveland Public Library and go from there to "The Necrology File".
Your project sounds very ambitious, (and worthwhile!) Good luck!
Lois Ralph