Hmm. Getting really quite suspicious here now about the name "Arlington". I'm noting a few things:
1) The closest marriage I can find for Anna is this one, in 1883 - note she is "Kroffig"
https://familysearch.org/pal:/MM9.3.1/TH-1961-29894-8490-89?cc=1804002Note witness "Charles Apelnstall"
If this is her then she was actually b. Dec 1852 according to the 1900 census:
https://familysearch.org/pal:/MM9.1.1/M9GH-QYK2) There is this family "Aplustrell" in 1860, with an infant son son "Louis C"
https://familysearch.org/pal:/MM9.1.1/MDK2-7V3Apalestel in 1870:
https://familysearch.org/pal:/MM9.1.1/MNX9-7SZI can't find them in 1880 - I can later find at least son Ernest, the remarriage of the father, but no trace of "Louis C".
http://etat-civil.bas-rhin.frNow, here we can search the births for Strasbourg.
4 Dec 1852 - Anna Kroffig
she was the daughter of Jean Joseph Kroffig and Salome Amelie
Aplustill.4 July 1848 - marriage of Jean Joseph Kroffig to Sophie (mistake?) Amelie Aplustill. Hard to read but shows that she was b. 3 Sep 1816, father (?name) d. 27 August 1838, mother Marguerite Salome Tr????r d. 26 May 1832 (all events in Strasbourg()
15 Feb 1831 - birth of Charles Aplustill to Jean Aplustill aged 40 and Margeurite Salome Tranner
3 Sep 1816 birth of Salome Amelie - to Jean Aplustill aged 26 and Marguerite Salome Tranner
So if "Lewis Charles Arlington" was actually "Louis Charles Aplustill", he was cousins with Anna Cushing nee Kroffig as his father Charles and her mother Salome Amelie were siblings.
As to "Uncle Charlie", there was a man going by the name "Charles Martin Applestill" who appears to have been born slightly after the 1870 census sometime. In 1910 father Charles b. France is living with him:
https://familysearch.org/pal:/MM9.1.1/MV2V-F8VNote wife "Katy" and son "Herbert" - as mentioned in the letters.
If this is the right family, it appears the first wife of Charles (Louis C. Aplustill's mother) died probably mid 1870s - that might have had something to do with his going to sea/changing his name.