Peter
Firstly I would like to point out that I do all my own research & only quoted a will summary to make it easier to read the message - I have a full copy of the will.
Secondly I only want my tree to be as correct as possible so any proof that I have gone wrong would be greatly appreciated.

Now to continue with your list:-
Robert Corlett was a sawyer/joiner not a labourer(as stated on 1841&1851 censuses).
John born 1800 died 1833
Robert b 1807 m Lydia Stott in Liverpool & has a son Claudius French Corlett - I have no idea where this name comes from so Lionel makes a good point about the name (I have not done any research on the Stott side so it may come from there).
William Thomas Corlett b 1807 d 1887 married Sarah Roberts in 1830 in Liverpool.
Charles Edward Corlett born 1809 d 1810
Edward Corlett born 1811 d 1827
Elizabeth Corlett b 1813 married Richard Edward Callister in 1834 Braddan
Maria Elizabeth Corlett b 1820 married John Richard Cubbon in 1839 Braddan and later marries Peter Moore in 1860 Braddan
Jane Corlett born 1822 d 1843
I don't think there is a Susanna.

Robert Corlett & Elizabeth Cottier are buried in Old Braddan Churchyard along with their children
Edward
John
Jane
Elizabeth
William Thomas (cabinet maker) & his wife Sarah & their daughter Emma Elizabeth
I have a photo of this gravestone.

I am certain about the above information as my 2nd great grandparents were William Thomas Corlett & Sarah Roberts and also Richard Edward Callister & Elizabeth Corlett - their children (being 1st cousins) marrying in 1880 in Liverpool.

So returning to Elizabeth Cottier - perhaps Lionel has a link to the will of William Cottier and we can try to prove her parentage.

If you would like me to expand on any of the above please let me know.

Thank you for your interest.
Carol (Mike is my other half)