Hannah Danforth (Allen) - Hannah's husband and children

Hannah was only married to Samuel Danforth Jr. not to his father Rev. Samuel Danforth (he died when she was one year old!).
It seems unreasonable to assume she had another husband named Samuel Danforth (the cousin of Samuel Jr.) and she certainly wasn't the mother of all the children listed as their birth dates span multiple generations including 32 years before she was born until she was age 61 and several just a few months apart !

How can we straighten this out?