I believe that when Scripture talks about the sins of the fathers being visited on future generations it is not related to spiritual life but to our natural or human existence. For example here in South Carolina the children of Governor Sanford are certainly suffering because of their fathers sins. In North Carolina the children of Edwards are certainly suffering because of the sins of their father. If he winds up in prison it could affect more than one generation.
.....visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me; Ex 20:5
I believe a good example of what is meant by this is what came upon the the children of Israel for the sins of their fathers because of the evil that they did to their brother Joseph, in that they betrayed him and sold him into bondage (Joseph is a fascinating type of Christ):
And he said unto Abram, Know of a surety that thy seed shall be a stranger in a land that is not theirs, and shall serve them; and they shall afflict them four hundred years; Gen 15:13
And God spake on this wise, That his seed should sojourn in a strange land; and that they should bring them into bondage, and entreat them evil four hundred years. Acts 7:6
It was exactly the fourth generation that came up out of Eygpt.