Going round and round and round here aren't we?   ...  The sin in a child is from imperfection of the sins of the fathers causing mistakes and unwitting damage to the child. 

Going round and round ... yes, but that's the nature of your argument.

If, as you say, the sin of a child who is born sinless is

from imperfection of the sins of the fathers causing mistakes and unwitting damage to the child

how did the fathers (and mothers, incidentally) become 'sinful'?  You can run this cycle back and back as far as you want, but ultimately you have to be able to answer how that sin actually came to be present in what must, if your argument is correct have started out as a 'sinless' world.