Elizabeth may be nee BRADER not Brady and then married a Brader after David died.
Richard Brader COXON Birth Reg March 1848, Horncastle, 14 455
Henry did not die.
1851 Census
Horncastle, Lincolnshire
133/2107/135/39
John BRADER, 66, Head, Mar, Ag Lab/Pauper, born Loenton
Charlotte Brader, 54, Wife, Mar, born Boston
Henry COXON, 5, Grandson, born New York, Lincolnshire
1861 Census HARRIET Brader age 25 is with John/Charlotte down as Daug so it all ties up
ELIZABETH Brader Baptised 24 March 1822, St Peter, Wildmore
Parents JOHN/CHARLOTTE, Fathers Occp Cordwainer, abode High Toynton Allotment
(FreeREG)
John BRADER Married Charlotte WINGATE, 31 March 1818, Coningsby, Lincoln
(Familysearch.Org)