Hello isiwig,
I don't have any connection, but I thought this was interesting and took a look. I began by looking at the crossed out names that you mention from the 1911 census - Albert and Arthur. I think that both of these married in the preceding decade. Albert Edward married Martha Alice Leeming in 1904 at All Saints church, Habergham Eaves, and - as you point out - the family resided in Giles St, Padiham in 1911. I *think* Arthur married Ada Wilkinson at Padiham St Leonard in 1903 with the family living in Lawrence St, Padiham in 1911.
So I think both children married with the Waddington name and also used it on the 1911 census.
So I think the next step would be to look at the marriage details for Albert in particular, and see who he names as his father. The marriage registers for All Saints are held at the Lancs Record Office in Preston, so if you live near there you could take a look and avoid the certificate fee. I live too far away to be able to help here.
The other interesting thing I noticed is that Sarah is described in 1891 as married, rather than as a widow. There could be various explanations for this, desertion being one, and raising the possibility of the father of the earlier children not being Richard McCartney.
Anyway, I hope this helps, I'd be interested to know how you get on.
Tim W