There seems to be quite a contrast between Edward & Edith Annie.
A possible birth registration for Edward - poss the most likely Veitch or Storey candidate on
www.freebmd.org.uk ?
Henry Edward Veitch Sep quarter 1873 Alnwick
He then appears as Edward Storey in 1881, with Henry & Elizabeth Storey & may be the Edward Henry Storey who marries Margaret Jane and turns up in Northumberland as Storey in later censuses. Can't see him as Edward Veitch but may have missed him.
By contrast Edith Annie does not seem to turn up in the records as Storey at all, and has not been found living with Henry & Elizabeth (I suppose she could have done so between census years). This of course is not proof, but at this stage I would keep my mind open to the possibility that perhaps even if Edward was the child of Henry, Edith Annie may not have been.
I noted earlier that Elizabeth Veitch's place of birth was Scotland in 1891 & 1901. In 1881, however, it is given as Berwick, Northumberland. In 1911 it is further south than that.
The birth of an Elizabeth Veitch is registered in Berwick in 1847 - can't see a later one in Northumberland in the right time period. Perhaps she knocked a few years off, perhaps she really was born in Scotland (you can check Scotland's People - baptisms for RC & Church of Scotland only as Scottish civil registration did not start until 1855) or perhaps she was registered under another name.
You could also see if anyone is researching Edward, as they may know something about the origins of both children.