It wasn't a document, it was a card index (hundreds of cards in wooden drawers) which had been compiled from shipping records, newspaper notices of passengers arriving, etc. I noticed how many of the cards noted children of convicts, but I think these were unaccompanied children, and therefore named. If Sarah's children were not named in the shipping record they wouldn't be in the index.
It might be worth looking to see why her Cert of Freedom was cancelled the first time:
LYNCHEY Sarah Mary 1835 47/0749 2 Nov 1847 4/4410 1025 cancelled
LYNCHEY Sarah Mary 1835 48/0129 6 Mar 1848 4/4410 1025 TL 43/1994