Phew, so much info, thanks!
I totally agree that we are dealing with two couples here, James and Elizabeth and then William and Sophia. Isaac and Abraham are both children of James (whether that's the same James is another story); William and Sophia Paskins did not have any children called Isaac and Abraham, so why would they be listed as the parents in the poor law records? As I said in my original post, the surname in the poor law records is Parkins, not Paskins, but I cannot find any William, Sophie/Sophia, Isaac or Abraham Parkins in Sussex so would like to make the inference that they are Paskins'. Interestingly, there is a removal order for a Parkins family in 1840 on the poor law records that is most definately a Paskins family ...
From Barries geneology there is a James Paskins in the 1821 census listed - 3 males and 1 female. You would assume the 1 female is his wife, but then where has Eleanor gone?