George Jones, 19 in 1851, is 10 in 1841, and he and presumed sister Elizabeth from 1841, are probably Ann's children from her first marriage.
In 1851 census George Jones is from Fernley Heath, have you tried to find a baptism for him?
If there is no Father's name on the marriage certificate then either Ann has forgotten/does not know, or she was illegitimate.
As Ann is already with George in 1841, they could have been married before civil registration.