From census data of Ernest and Dolores, consistently indicate his birth in Canada, as does the marriage cert. See second cert- did Ernest have a brother William James - seems to be son of James Thomas Hamilton and Harriet Lenora Keyes?
Not what you were asking, but confirms Dolores' name and her parents:
SOURCE: Montana, County Marriages, 1865-1950, database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:F37X-Z9N), Ernest Hamilton and Doloras A. Mcnamara, 18 Jul 1900; citing Marriage, Butte, Silver Bow, Montana, county courthouses, Montana; FHL microfilm 1,906,798.
Ernest Hamilton
Age 27 Birth (Est) 1873 Bloomfield, Carleton, Canada (NB)
Father J. T. Hamilton
Mother Harriet Keyes Hamilton
Marriage 18 Jul 1900 Butte, Silver Bow, Montana
Spouse Doloras A. Mcnamara
Age 22 Birth (Est) 1878 Virginia City, Storey, Nebraska
Father Thomas Mcnamara
Mother Mary C. O'Connell Mcnamara
SOURCE: New Brunswick Provincial Marriages 1789-1950," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVBN-7L59), William James Hamilton and Julia Anne Ebbett, 05 Nov 1936; citing Woodstock, Carleton, New Brunswick, Canada, p. , Provincial Archives of New Brunswick, Fredericton; FHL microfilm 2,320,231.
William James Hamilton
Age 70 Birth (Est) 1866 Rosedale, Carleton, NB
Father James Thomas Hamilton Birth: Queens Co., NB
Mother Harriet Lenora Keys
Marriage 05 Nov 1936 Woodstock, Carleton, New Brunswick, Canada
Spouse Julia Anne Ebbett
Age 67 Birth (Est) 1869 Bear Island, York, NB
Father John Hagerman Birth: Bear Island, York, NB
Mother Sarah Jane Manuel
Certificate Number 5886
IMAGE AT: https://familysearch.org/ark:/61903/3:1:3QS7-89MN-NWRB?mode=g&i=1335&wc=M6K3-8NG%3A284558801%2C284575401%2C284575402%3Fcc%3D2001065&cc=2001065