I think this might be your family:
William Hamilton, born Dec. 31, 1894, Waterville, York Co., NB, son of Melvin Hamilton & Sarah Jane Wilcox. (Provincial Archives of New Brunswick records)
1901 census - Southampton, York Co., NB
District # 25, o-2, page 15
Melvin Hamilton, 34, b. April 17, 1866, NB, Church of England, Farmer
Sarah J., wife, 31, b. Dec. 7, 1869, NB, Baptist
Ada M., daughter, 10, b. May 2, 1890, NB, Church of England
Ethel, dau., 9, b. June 6, 1891, NB, Church of England
Samuel, son, 8, b. March 25, 1893, NB, Church of England
William, son, 6, b. Dec. 31, 1894, NB, Church of England
James, son, 4, b. Nov. 29, 1896, NB, Church of England
Nettie, dau., 2, b. Sept. 13, 1898, NB, Church of England
George M., son, infant, b. March 9, 1901, NB, Church of England
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1881 census - Southampton, York Co., NB:
Samuel Hamilton, 62, b. Ireland, Presbytarian, Irish, Blacksmith
Charlotte, wife, 58, b. NB, Baptist, French
Melvin, 23, b. NB, Baptist, Irish, Blacksmith
Ada, 21, b. NB, Baptist, Irish
Juletta, 14, b. NB, Presbytarian, Irish
Martha Wilson, 30, b. NB, Presbytarian, Irish, Servant
John Loundsbury, 18, b. NB, Baptist, English
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1881 census - Southampton, York Co., NB:
William Wilcox, 34, b. NB, Baptist, Farmer
Mary, wife, 36, b. NB, Baptist
Sarah, 12, b. NB, Baptist
Martha, 10, b. NB, Baptist
George, 8, b. NB, Baptist
Edith, 6, b. NB, Baptist
Mary, 2, b. NB, Baptist
Pearl, 5 months, b. NB in Nov., Baptist
Caroline Bull, 26, b. NB, Baptist
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Upper Queensbury Cemetery, York Co., NB:
Charlotte Hamilton, wife of Sam, d. Sept. 21, 1887, age 62 years.
Ellen Amelia Hamilton, dau. of Samuel & Charlotte, d. Oct. 16, 1856, age 12 years.
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Penniac United Church Cemetery, York Co., NB:
Melvin C. Hamilton, 1865-1944
his wife, Sarah Jane, 1869-1937
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1921 census - Silver Hare Island, Bonavista Bay, Newfoundland:
John Button, 48, Church of England
Chrisina, 18, Church of England
Harrison, 13, Church of England
Charlotte, 11, Church of England
Kenneth, 8, Church of England
Belah, 5, Church of England
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I'm not related. I just thought I'd see what I could find for you.