I see that the death for Peter shows his father as Peter also and his birth as the date you show April 8, 1835
BUT I also found the marriage for Peter and Adella Ruoussel July 1, 1880 and it shows Peter as a blacksmith which seems right from the census and he is shown as age 45, divorced and his parents names are shown as Jos. Sabourin and Morice Hesmores
the Hesmores is a bit hard to read but that looks like it. So perhaps his father was Joseph Pierre ?
This record is in Vermont vital records at ancestry.com