Well, you can narrow it down a little more, Hiram is still living with his parents in the 1860 census, no sign of a wife, but by the 1865 NYS census he is again living with his parents, listed as "now widowed" married one time with two children. Only Ida is with the family, however, age 4 - she is listed as Gdaughter. There are other children, Hiram's brothers and sisters. Perhaps there is a very young child who is in the care of his late wife's family.
BTW, Hirams parents claim to have had 14 children.