So what you appear to be saying Forfarian is that Margaret H H Robertson was in reality Lawson not Robertson at 1881?
I am saying that the child listed as Margaret Lawson in the 1881 census is the one whose birth was registered as Margaret Haldane Henderson Robertson in 1870. It's not a case of 'reality' or a case of one name being 'correct' and the other incorrect'.
I've looked for the Kinfauns kirk session minutes on one site and it said: Sheriff Court paternity decrees .....
I think I know which site you must be referring to. If so, it is a very useful site whose owners have been making available online the results of paternity cases from records of proceedings in the courts of law, and it deals only with cases which got taken forward for legal action. However it is most emphatically
not not the same thing as the Kirk Session records.
The Kirk Sessions were concerned with two things. First, a fundamentally doomed effort to stamp out sin in the form of fornication, which they did by trying to shame and humiliate those caught out sinning. Second, ensuring that illegitimate children did not become a charge on the parish. In most cases, the errant father admitted paternity and that was sufficient.
In some cases, however, a man accused of being the father of a child would stick to his denial, and in a few of those cases the mother took the case to court, usually to win the legal right to have the child's maintenance paid for. Those are the paternity cases referred to on the site you have found.
The records of the Kirk Sessions are held in the National Records of Scotland and as I have said they can be accessed there or in some other local archives. They have been digitised but they have not yet been made available online, though I understand that there are plans to make them available eventually via Scotland's People.
I checked the catalogue of the National Records of Scotland at
www.nrscotland.gov.uk and I see that the Kinfauns Kirk Session minutes for the period in question have survived. Whether they actually contain information about Bathia Robertson's illegitimate children I cannot say without looking at the actual documents.