I may have solved the Frederick ROTHERHAM problem. I found an entry for March 1887 recording the death of a Frederick ROTHERHAM, the age at death is given as 28 years. Now this would explain why when I ran searches on the England and Wales Census 1901 against Frederick and Sarah Ann ROTHERHAM (née BELLAMY), predicted dates did not agree. I am still using conjecture, but will trust it for the time being. Of course there is still the problem of little Frederick ROTHERHAM, who according to the England and Wales Census 1891 would have been born in 1888 or 1889.

Updates:
2005-12-15 Further research has shown this data is probably NOT linked to my family. This data may prove useful to other researchers so I will retain it.