Using census information I believe Henry's mother is Mary Peabody.

Henry's mother Mary Peabody (maiden name could be Pincumbe) worked in Detroit Michigan as a teen and became pregnant. She return to Canada and had Henry when she was 19 years old. She was not married at the time. She them married Thomas Peabody. The 1880 census has Thomas and Mary Peabody living in Clinton County near Lansing Michigan.

The censuses of 1851 and 1871 list a John Pinkham living with Thomas and Mary Peabody. This could be Mary's father.

Henry Pincumbe's lastname was Peabody in the 1851 census and by the 1870 census he had changed it to Pincumbe. Henry names his first child, John Pincumbe, possibly after the John Pinkham in the 1851 and 1871 censuses.

Henry's son Elgin Pincumbe changed his name to Peabody after living with his Grandmother, Mary Peabody near Lansing Michigan.

The scanned census images are large jpg's, 100,000 to 200,000 bytes each.

Census Information

Scanned Census
Jpg Images
1851 Left Side

1851 Right Side

1851 Canada Census
Rochester Twp, Essex County, Ontario

Thomas Pebody 44 (farmer)
Mary Pebody 34 (wife)
Henry Pebody 15
Birtin Pebody 13
Mary Pebody 7
Thomas Pebody 1
John Pinkham 66 (bricklayer)
1870 Page 1 (Headings)

1870 Page 2 (Henry & Catherine)

1870 Page 3 (John & Elgin)

1870 US Census
Fair Haven Twp, Huron County, Michigan

Henry Pinkum 35 (farmer)
Catherine Pinkum 25 (keeps house)
John Pinkum 5
Elgin Pinkum 4

This census includes other relatives. Graves, Harder, and Grant. Catherine Pincumbe's sister Mary, who married Charles Grant is on page 2, line 33.
1871 Left Side

1871 Right Side

1871 Canada Census
Rochester Twp, Essex County, Ontario

Thomas Peabody 64 (farmer)
Mary Peabody 55
Joseph Peabody 20 (farmer)
Franklin Peabody 10
Martha Robinson 4
John Pinkham 84 (bricklayer)
1880 Top Half (Headings)

1880 Bottom Half (Peabody's)

1880 US Census
Riley Twp, Clinton County, Michigan

Thomas Peabody 75 (farmer)
Mary Peabody 66 (wife, keeps house)
Henry Young 16 (hired man, works on farm)
Sarah Peabody 27 (daugher in law, at home)
Chas. Peabody 7/12 (grandson)
1900 Left Side

1900 Right Side

1900 US Census
DeWitt Twp, Clinton County, Michigan

Elgin Peabody 34 (day laborer)
Ida M Peabody 28 (wife)
Pansy P Peabody 11 (daughter)