Going back to what we have:
1841
Lancashire, Liverpool
Cookson Street
Ann McFarland (sic) 38, yes
Lawrence 13, yes ...where is his christening? and where does he dissappear to?
Samuel 11 .... christened 2 May 1830, born 25 May 1828, Chesterfield
Catherine 11....christened 2 May 1830, born 8 Apr 1830 ditto
George C 2, yes
Samuel and Catherine christened the same date , birth days different! Same age on 1841

Where is Francis b 1826?
I've found a Samuel but he's born in Liverpool circa 1829... maybe Samuel thought he was b Liverpool as he had lived there for a while.
In 1851
Ecclesall Bierlow
64 back Lane?
Wm South , head, mar, 52, edge tool maker?, b ?? Yorks
Sar, wife, 50, Shefd …Sheffield?
Josp, son, unm, 26, edge tool striker b ditto
SAML MacFarlane, son-in-law, widr, 22, French polisher and app. B LIVERPOOL
Samuel M = Mary Ann South in 1848 Ecclesfield Barlow
vol 22 pg 83
So Samuel snr is b 1806ish, Jersey ...ends up having sons Francis (1826) and Lawrence (1828) b Liverpool, moves to Chesterfield has three more children Samuel (1828), Catherine(1830) and Jane (b and d 1832), then moves back to Liverpool and has George (1839) and Charlotte (1843).
But how can he have Lawrence and Samuel in the same year ? It's possible I suppose unless Lawrence's age is off in the 1841.
Chrissy ...do you have Ann's maiden name?
I wonder what George's middle initial "C" stand's for.
deb