One thing that might help you in looking for Catherine or Caterina, assuming that she emigrated from Italy around that time period, maybe 1905 to 1910, is that you can search the Ellis Island database in one step:http://www.jewishgen.org/databases/EIDB/ellisgold.html
I put in the name Caterina Neruina and chose sounds like, and it came up with only 15 or 16 matches, mostly Marano or Marino or Merino or Marana and one Murania. If you do the same search and go through the manifests, you can eliminate some by personal characteristics (ie already married) or by year of emigration which will probably leave you with about half a dozen or so.
One of those listings is for a Caterina Marino, 20, who arrived 1906, who was a domestic and going to New York, that might be worth looking at further.
There would seem to be two possibilities - one that she met Michael after emigrating to New York, and one that she knew him back in Italy and specifically emigrated to marry him once he had earned money to establish his own household. If she came over specifically to marry him, she might not appear on the 1910 census. If she met him in New York, then she might well be on the 1910 census. Are there any family stories about how they met?
Easiest would be if Dominick's death certificate has a correct spelling of her surname. But if not, using Ellis Island and cross checking possibles might be another way to narrow down the possible list.