Hi Peter,
What is it you are trying to prove?
Is the information that you gleaned from the IGI from extracted records or member-submitted?
In as far as one can prove anything before 1837, it is always recommended that the original parish records be consulted. However, if what you have found already came from extracted records, then you may not find much more than is already contained on the IGI. Post 1812 baptisms may contain the maiden name of the mother, but not always. However, it will contain the occupation of the father and where they lived. But there again, the father could have changed his occupation with the passing years! And they could have moved to a differently-named part of the town/village or parish.
Prior to the introduction of printed registers in 1812, then you are at the mercy of the incumbent with regard to the detail contained in the register.
For marriages, there are no parents' names included ( no box for them) and occupations likewise are often missing.
To link the children to their parents, apart from baptism records, there may be a will. No-one should be discounted as too poor - sometimes they surprise us.
Burial records of children who died young may record their father's name. There may be memorial inscriptions as well. They could help.
Have you looked at the online catalogue for Hampshire Record Office? See here:
http://www.hants.gov.uk/record-office/catalog/index.html But it really depends what you wish to prove
Nell
