In 1891, widow Catherine and her family are in Wingate, which was part of the Easington Registration District but in 1881 the family were living at Chilton which was a part of the Stockton Registration District.
From the FreeBMD list of deaths between 1881 and 1891 there does not seem to be one for William which matches exactly. However, from those which are listed, the most likely one seems to be that which is registered in Stockton in 1882 Q1 10a 51. The problem is that the age of 52 is wrong on the GRO Index. There is a possibility that the age could have been entered wrongly when the lists were originally submitted and that the actual entry at Stockton might say something different.
You could use the following link (or you could telephone) to ask the Stockton office to check for you if it is your William. There does not appear to be another suitable William Etherington, in the Stockton area, on the 1881 census
http://www.stocktonroots.co.uk/contact.aspxIt might be worth a try, if only to eliminate it. GF