I am researching my Wife's Dingman family, and have been very successful.I would bet your Peter Dingman is related to her family.My wife's g gf Geroge Dingman was born in Cramahe, Northumberland, Ontario in 1866 to Garrett Dingman and Phoebe Puffer. He then emigrated toNorth Dakota in the 1890s. Garrett Jr. (born 1827)was the son of Garrett Sr (b. 1794)and Ann Sabins. I would bet that your Peter was the son of one of Garrett Sr.'s brothers: Jacob, John, Peter, Issac, Samuel or Jared.
I see your Peter and Rachel Dingman, with children John, Henry and Mary, were living in Cokato, Wright, MN in 1870.
If that sounds correct, let me know and I can give you quite a bit more information.