I think James FOORD possibly married Susan DRAKE in 1837 Canterbury registration district and it is possibly they who appear in the 1841 census at North Lane, Canterbury. What happened to her is, as you say, a mystery at present but I do think it is the same James FOORD as that with Sarah in 1851 and 1861. In 1841, one of James' neighbours is an Elisha HOMERSHAW (or whatever it says) and they are still living next to one another in 1851 so I think it is too much of a co-incidence not to be the same James FOORD. Perhaps James' first wife, Susan, didn't die hence the absence of a marriage to Sarah
I can only guess that the children used the surname FOORD - whose to say that they even knew their parents weren't married if that was the case - but the GAWLERS preferred their relatives to be known as GAWLER (possibly because they legally should have been). I don't think any of us can say for sure but we can just look at the different possibilities/scenarios.
Could this be a possible for your Sarah GAWLER in 1841 I wonder being, as you say, she doesn't appear with her supposed parents, Robert & Sarah, in St Gregory
1841 Prospect Place, St Peter, Thanet
Elizabeth KENNETT 20 charwoman b.Kent
John 9m b.Kent
Sarah GAULLER 12 b.Kent
HO107/468 folio 23 page 4
Casalguidi
