The missing child (John) from 1958 and Tom's son (Tom Jr.) were both victims of "Diploma", the man Tom Sr. suspected in the disappearance of his child. Diploma worked with Matthew (John's father) and saw John (who was mentally impaired) as a burden to Matthew. It's insinuated that John was his first victim, and Tom Jr. was his last.
Matthew marries the waittress who helped him during his search, brings his other children to live with them, and tells them John went to a special home for kids like him. Later, he tells them John died of illness.
During his interrogation of Diploma for the 1958 crime, Tom Sr. is able to get Diploma to reveal a clue that helps him find where his son was killed/buried (at the carnival), and he and his wife are able to find closure.