May I ask why you think James Alderson, Father of Thomas 1849 South Broom had a Westmorland connection?
I presume this is Thomas;
ALDERSON, THOMAS, Mothers mn RICHARDSON
GRO Reference: 1848 M Quarter in AUCKLAND UNION Volume 24 Page 13
Frances Jane I presume was widowed when she married 1847, previous Marriage 1843 to John WALTON .
So James Alderson had died by 1851 Census so we have no pob for him.
His Death Reg
ALDERSON, JAMES age 46***
GRO Reference: 1850 M Quarter in AUCKLAND UNION Volume 24 Page 4
1841 we have in South Church Durham;
James Alderson, 35, Pitman
Mary, 35
Mary, 14
Hannah, 11
Rachael, 8
James, 5
Elizabeth, 10 mths
All not born in County except for last 3 children.