It was Amy Phillips who died as reported.
I would think that spelling her name as Anne was a reporter or papers error (probably not a 1st hand account).
The younger John Joseph Smith in 1861 census is probably
1861 Census
Shropshire, Ellesmere, District 7, p38/41 [references from Ancestry pages]
John Smith, 10 Pupil at the Vicarage, Ellesmere, born Llangollen, Denbighshire
And a guess for the 1871 census - though the age is slightly out - it would seem likely if he received money and property from his mothers death
1871 Census
Cheshire, Tranmere, district 3 p22
John Smith, boarder, 23, land and property income, born Llangollen
After that there are so many John Smiths in England & Wales it would be hard to find either the father or son - not including any chance that they went back to Ireland.
I have not yet found the elder John Smith in 1851 so am assuming he's in Ireland
I would say that Amey Smith probably stayed in Llangollen to help her mother Amey Phillips [died 27 Aug 1857] run the hotel.
Im still trying to trace the whereabouts some of Amey Smith/Phillips siblings
Can you share any details of Abigail Smith's time after 1851?