The dates in the following are way off, but going by my index to the 1851 census where Sophia is on her own in Brighton with some of the children, William's son William (born Brighton 1837) has moved to Canterbury. The 1851 index entry for William 1837 is preceded by what may be his father William (stated as born Canterbury) whose birth year is given as 1814.
Seeing that Sophia's birth year on the 1851 index and transcript (she is shown as aged 48 & born Pevensey c1803) bears no resemblance to 1841 (born Sussex 1811), and that William was alive until at least 1844 to father Robert born 1845, it must be worth your while to check the Canterbury entry on the actual 1851 census to see if this could be father and an elder son together.
Sophia was identified by the other children with her by the way.
They were all living 18 Montague Street, Brighton. HO 107 1644/ folio 272.
Sophia died in Brighton in 1856. Roy G