Hi Darryl,
I've been doing a bit more digging and I think you've got it right.
It looks like the family moved from Norfolk to Durham around the 1860s/1870s, presumably for work which is usually why families moved in those days. I haven't checked each and every census, but from what I can gather, you seem to have the family relationships correct.
I did manage to find Thomas W b 1900 with father George W b 1871 - they are in the 1901 census mistranscribed as Moury. But it is definitely them. George W looks to have married Mary Todd in 1894. John Money b 1844 married a Susannah (maybe Parnell in 1866).
Something I can't quite work out, is how the family had buildings named after them. Do you know any stories about that? You would expect them to have been a family of some importance to have buildings named after them, whereas your family seem to have been labourers and coalminers. Perhaps they helped to build the buildings and for some reason had them named after them?

No particular rush for any documentation - I just wanted to check that you'd got it right and from what I can see, it looks like you probably do. It might be wise to check to see if there are any other Moneys with the same names and birth years as yours just to ensure that you are definitely correct, and don't have families and children mixed up. Documentary proof is always necessary of course.