I don't know if you still need this info, but here it is. There is a Freeze Cemetery in Latah Co. You're family is listed there.The name Pickering is spelled with a "D" instead of "P", could be a typo. This info can be found at usgenweb.org, then go to state, then county, then a listing for cemeteries. Don't know if all these names are yours but they are all from this cemetery.No dates on the twin babies.
Row 10: Baby Dickering, Baby Dickering, Mollie Dickering 1853-1892, Lillie A. Bingham 1832-1881, J.N. Bingham 1830-1893 Row 28: Mabel V. Bingham 1879-1953, J.W. Bingham 1871-1946 Row 29: Bingham, Mary E. 1880-1953 Mom, Frank H. 1877-1961 Dad God alon understands
Also under "Freeze Cemetery Veterans": John N. Bingham