Hello from Bermuda. From the church registers in Bermuda I found the following. 19th Century Church Registers of Bermuda compiled by Hallett Page 203 - Hamilton Parish baptisms:
Brown, Elmer Winfred - father: Edward Thompson - mother: Adria - baptism date: 1883 Jul 20 - Hamilton Parish - comment: father aFarmer.
Brown, Elmer Edward James - father:Elmer Winfred - mother: Effie Winifred - baptism date: 1906 Jan 14 - Hamilton Parish - comment: father a Farmer.
Hamilton Parish groom marriages page 244
Brown, Elmer Winfred - of Hamilton Parish - married -Lightbourn, Effie Winifred - of Hamilton Parish - date: 1901 Sep 12.
These are the only records I could find and I have not idea if they are what you are looking for or not. This book only goes up to about 1909.After that date you would have to search the records at the Registrar General's office in Bermuda as they would not be public yet. I did not find anything at all under Brown, Diane nor Smith, Dorothy.
Have you tried www.ellisisland.org to see if they went thru Ellis Island upon their arrival in the USA? Sorry I cannot be of more help. Sincerely, Judy