Good hunting Ian, there appear to be lots of loose ends.
You have August Joachim Danielsen, the son of a prosperous family of merchants (perhaps also ship owners) who died within 3 years of his marriage (1857-1861) It was not in the UK so was it in Denmark or an accident at sea? The 1861 census suggests that his new wife Fanny and son returned to her parents' home in London for a period of mourning.
You do not know where his wife Fanny and son Josia(s or h) were in 1871 & 1881, so cannot say where the son was educated, but their status sugests a private school. As you say, the details may have been mistranscribed so check out the cook's name (on the 1891 census) and the see if she could have also been with them in 1881.
You know mother and son were of independent means and were living at the Yews in Deal in 1891. That property is presently up for sale so you have pictures of it on the Internet.
http://www.rightmove.co.uk/property-for-sale/property-24917824.htmlFanny died in Bath in 1900 and in all probability left a will. Thats well worth applying for through the Probate Office.
You also know Josia(s or h) had 2 children, Cecil and Ronald, so check out Noaleen Mullholland who is on Genes like you are and shares your interest.
A challenging on-going task isnt it? Roy G