Background (I hope you don't mind Poozan) the middle names might help somewhere along the line. Although you have all this info, it might help us 'build a picture' and figure out some clues

"Margaret Maxwell ANDERSON" Your gt-grandmother
http://www.rootschat.com/forum/index.php/topic,447448.15.htmlHer siblings known were:
Florence Guild ANDERSON b abt 1849 Glasgow, m singapore 1871,
(added, see reply #19)John ANDERSON b 1852 Rothesay, Bute, died 1924 England, Knighted in 1912
Marion Fullerton ANDERSON b 1854 Rothesay, died 1933 England
Singapore newspaper
http://shrinkalink.com/36281Margaret Maxwell ANDERSON married November 9th 1875 in Singapore, to Thomas CUTHBERTSON.
She was stated a the "third surviving daughter of the late John ANDERSON"
http://shrinkalink.com/36282In 1901, the Cuthbertson brothers attended a wedding in London, Eng;and in 1901, of John ANDERSON age 48 (b abt 1853), recent M.L.C at Singapore.
John married Winifred Ethel Dunbar Pope on 16th January 1901
London Marriage Record
John' age 48 was a widower & his father was stated as John ANDERSON, Master mariner and civil servant (deceased)
His first wife was dau of Admiral BUSH of Siam, she died in 1894 I think (Singapore Newspapers clipping)Singapore Newespaper - Obit for Marion
http://shrinkalink.com/36283Thomas' brother JOHN CUTHERBERTSON married a Marion Fullerton ANDERSON.
When John CUTHBERTSON's widow died age 80 in 1933 (b abt 1853) her obit states:
Her father Captain ANDERSON lived in Singapore where his wife had a small school, known as the Raffles Girls School. Of their (Captain john Anderson & his wife's) children:
2 daughters married the CUTHBERTSON brothers, John & Thomas.
1 son John later Sir John ANDERSON ...commenced his Straits career in Govt Service, then Partner & Head of Gurhrie & Co.
http://shrinkalink.com/36284ANDERSON, Sir John, Knt.— Cr. 1912.
Son of John Anderson, Esq., of Rothesay, Buteshire
b. 1852 ; m. 1901 Winifred Ethel Dunbar-Pope, dau. 1
of John Billing Pope, Esq. Sir John Anderson was an
Unofficial M.L.C. Straits Settlements 188G-8 and
1905-9 and is a Member of the firm of Guthrie & Co.
Ltd., East India Merchants, of Singapore and London,
and Consul-Gen. for Siam in London ; appointed 2nd
Secretary to the Ministry of Health \9l9.—Eastcote
Place, near Pinner, Middlesex ; Bath Club, w. ; City
Carlton Club, e.c. ; 5, Whiitington Avenue, E.c.
http://www.rootschat.com/links/08dd/Article including information on Captain John ANDERSOn & his son John Jnr. and including the mention that Captain J sailed the SHANDON to Melbourne when he was 60 ish
Also, John Jnr - Sir John ANDERSON 1852-1924 - has an entry in the Oxford Dictionary of national Biography - which says:
He was a merchant, born at Rothesay, Scotland, in March 1852........"Eldest of two sons and three daughters of John Anderson (1793–1875), sea captain, and his second wife, Janet Halley, schoolteacher and a daughter of a Glasgow shopkeeper. In 1855 Captain Anderson sailed his small paddle-steamer from Scotland to Australia......His family joined him in 1856 and settled at Geelong before moving on to Singapore about 1859. Here Captain Anderson was eventually assistant harbour-master, and his son attended Raffles Institution until he was sixteen"I'm pretty sure I saw John Jnr stated as the ONLY son of John Snr in another of those links.
(Our Sir John not to be confused with another Sir John ANDERSON , who was a Governer of Straits, Singapore (b 1858-d 1918) & son of John ANDERSOn of Gartly Aberdeen)http://newspapers.nla.gov.au/ndp/del/article/5679080?searchTerm=Shandon arrives in Melbourne - there are voluminous hits for John sNR and the "Shandon" in the Ausie Newspapers.
http://www.wikiwak.com/texis/wcolz/viewcache.html?q=hms+bulwark+1859&h=375d41ec2f901f1e01d6d1aabd2b4dc7Shandon. Wooden paddle steamer, 186 tons. Built at Glasgow, 1853. Left Scotland on 6 December 1853 and arrived in Me!bourne on 24 April 1854 after a voyage of 140 days under sail. Later sold to. oveseas interests.
Death Notice in Aussie Papers for Captain John Snr.
http://trove.nla.gov.au/ndp/del/article/11520872?searchTerm=ANDERSON SHANDON
Janet ANDERSON, widow of Captain John, died in 1891 in Hampstead, age 76 (after the Census)
She appears on the 1891 Census in Hampstead age 75, b Scotland in household of her son-in-law Thomas CUTHBERTSON (who is a widower - he was later to remarry).
Cheers
AMBLY