I think having Edward/Edmund from Smethcott in 1851 (albeit with the wrong place of birth recorded!) is a step forward, as he has the gardener occupation that matches the marriage in 1852.
I wonder if sister Ann, still unmarried in 1851, went to South Africa as well and could be the Ann Rogers who appears in records for Richard junior there?

But I can't see anything in SA about her at all.
Sarah Rogers in Oxton in 1851 may have died in 1853
ROGERS, SARAH
Age at Death (in years): 64
GRO Reference: 1853 J Quarter in WIRRAL Volume 08A Page 286
Age up on that given in the previous census, but possibly more appropriate.
Buried, like William's wife, at Woodchurch (the parish for Oxton), 15 May 1853. I don't think we have an image anywhere.
https://www.familysearch.org/ark:/61903/1:1:F3T5-CN5The death certificate (available from the GRO as a £3 digital image) might clear up whether she was the widow of Richard the blacksmith, or not.
I am thinking that on Edward's second marriage, there may be a mistake for his place of birth.
He said Shropshire, but it was misheard as Yorkshire.