When Longmire and Vic visit the biological parents of the first child abducted there is the sound of a shotgun being racked. The shotgun he was holding was a break action, and would not make that noise. The noise heard would have been for a pump shotgun. The noise made by a break action shotgun is a simple click.
According to the Indian Child Welfare Act of 1978 (ICWA) a child who is a member of, or eligible for membership, in a federally recognized tribe would not be adopted outside of the tribe without the approval of the tribal council. The plan is to reunify the child with the parent, or simply to keep the child in the tribe being raised by other tribe members. A child would never be simply "taken away" and adopted by non-Indian races or cultures without diligent efforts being made to keep the child within the tribe. Hence, the entire plot would never happen.