Here are the two younger ones in 1891:
Woolmarket, Berwick
RG12/4268/6/5
Elizabeth Hogg, widow, 43, laundress, b. Berwick
Elizabeth, d, 15 general domestic servant, b. do
Edward, s, 10, b. do
Rentors, Lowhaughs, Berwick
RG12/4267/24/4
William Hogg, 38, ag lab, b. Berwick
Helen, w, 28, b. do
Edward, s, 7. b. lowhaughs
and 4 other siblings
I think that the first one is the one Barbara is looking for.
I've checked emigration but no obvious hit and nothing showing in the CWGC site. Could he have returned to South Africa

Gadget