Not related but admire what you are doing.Family search has a death record for John H Hart, an attorney, who died in Boise Idaho on 20 Sep 1916. He was born Jun 1840 in New York City. His parents were James Hart and Mary Rosich. He was widowed and buried in Nampa 23 Sep 1916.
Because of his middle name, he might be related to James HInmond Hart who appears on pages 124 and 125 ofA history of Idaho which was written after John's death. The article mentions that they had six surviving children having lost one. The glitch in this theory is James Hinmond Hart was married to someone else. Could be a connection of some sort.
In any case I think your John Hart married Emily J Sellick and had at least two children..