Hello Nessa
I can’t directly answer you question, but I may be able to help.
Moses Cook (b 1784) of a Rock is my great great great great grandfather. His father Joseph was born 1760.
I don’t have a record of any siblings pre the end of the C18th.
I assume the Jane Cook you’re referring to was the mother of a Thomas Oliver ( as given in the 1844 census).
Not sure how that helps - but it might provide a clue.