Hi. I'm not related to this family.I think Walter had Pierre's parents figured out correctly, based on Pierre's death certificate with the informant, Celina Ducharme, most likely being his wife.Here is a marriage for his parents from the Quebec, Vital and Church Records (Drouin Collection), 1621-1967:
Joseph Tetro dit Ducharme (Jean-Baptiste Tetro dit Ducharme & Flavie Aneau m. 19 Apr 1842Iberville (St-Athanase-de-Bleury), Quebec Genevieve Potevin (Francois Potevin & Isabelle Goyette)
So, in this case you are dealing with a "dit name", that being Tetro (Tetreau) dit Ducharme, with Tetro or Ducharme being used interchangeably in birth, marriage, death & Census records.
This couple had a daughter, Odile, baptized in the same parish:
Odile Tetreau, b. 4 Mar, bap 5 Mar 1844 Iberville (St-Athanase-de-Bleury), daughter of Joseph Tetreau dit Ducharme & Genevieve Potvin.
I did not find a baptism for Pierre, but I did find the family in the 1851 Census:
1851 Census of Canada East, Canada West, New Brunswick, and Nova Scotia about Adile Pétro Name: Adile Petro Gender: Female Age: 8 Estimated Birth Year: abt 1844 Birthplace: Bas Canada Province: Canada East (Quebec) District: Rouville County District Number: 25 Sub-District: St Alexandre Sub-District Number: 343 Household Members: Name Age Joseph Tetro44 b. 1808 Quebec; Farmer Genvieve Potvin33 -wife- b. 1819 Que Joseph Tetro10 -son- b. 1842 Que ** Adile Tetro 8b. 1844 Que Frs. X. Tetro6b. 1846 Que ** Edvige Tetro5b. 1847 Que Esther? Tetro3b. 1849 Que Theophile Tetro1b. 1851 Que Elizabeth Goyette61b. 1791 Que Francois Potvin47b. 1805 Que
Possibly your Pierre is son Joseph or Francois-Xavier. According to his death certificate, Pierre was b. 12 Feb 1846:
Joseph Ducharme in entry for Peter Ducharme, "Massachusetts, Deaths, 1841-1915"
name: Peter Ducharme titles & terms: event: Death event date: 30 Jul 1915 event place: Gardner,,Massachusetts residence: street address: gender: Male age: 69 marital status: Married occupation: birth date: 12 Feb 1846 birthplace: Canada estimated birth year: burial date: burial place: cemetery: father: Joseph Ducharme father's titles & terms: father's birthplace: mother: Genevieve Potvin mother's titles & terms: mother's birthplace: additional relatives: spouse: volume/page/certificate number: 289 film number: 2407808 frame number: digital folder number: 4284296 image number: 01904 https://familysearch.org/pal:/MM9.1.1/N44B-8SH
Joseph & Genevieve did have a son born on or very close to that date, and baptized on 13 Feb 1846St-Athanase-de-Bleury.The record is blurry, but I do believe it reads Francois-Xavier Tetro, bap 13 Feb 1846St-Athanase-de-Bleury, son of Joseph Tetro & Genevieve ?.