The 1851 census at Mill Rent? Ballaugh has :-

Charles Lawson 69 Ag. Labr & Tailor England
Mary 62 Wife Braddan
Mary Cottier Daugh. Widow 43 Ballaugh
Martha G.daughter 11 New York
Thomas G.Son 9 New York.

Other children are working away.

It appears you have the right combination with Lawson/Cottier. Thomas, 1810, is an official version of the register whilst the others in 1812 are someones embroidery.

You are still left with the question, which Thomas.

Len Faragher