Carol, would you mind having a look at the 1900 US census please?

There are a number of entries for a Bernard Cain travelling into New York Ellis Island, who looks like the father Bernard (b.1864) who was a mariner. For example there are two in 1920, aged 55, a bosun on the ship "Baltic", departure port Liverpool.

There was also a female "Cain", English, Residence Liverpool, arrived NY Feb.11th 1892 on the "Teutonic". Age on arrival 27yr, F., Married. I couldn't locate the Manifest to see who was travelling with her.
This could have been Bridget Cain als Doherty b.1866 who married Bernard Cain - except for her children in the English 1901 census said to have been born in Liverpool. But possibly an birthplace error because it said the same for son Bernard (b.c.1895 NY).

Thanks,
Sue