Hi fryerning
1) Yes, Emmeline Burke nee Riley was Louisa's sister.
2) Her husband was Robert Edward Burke, but I believe he answered to Edward.
3) It looks like Emmeline & her husband were living in Fremantle in 1908, not Boulder, so I don't think there is a Ballarat connection there.
4) But you're right that some details were probably assumed - it looks like William Titley's first marriage was in Queensland (these dates fit well):
The following info came up on the Ballarat board, where I had also place a query (I've asked for the source, but no reply yet):
BRISBANE.-William Titley is charged, on warrant issued by the Brisbane Bench, with deserting his child Mary Louisa Titley, care of Mrs. Doyle, Terrace street, New Farm, on the 6th September
last. Description :-A native of Victoria, a fencer, 25 years of age, 5 feet 7 inches high, slight build,
dark complexion, dark hair, clean-shaved except moustache, long thin face ; one of his eyes appears to be half closed. He was in Melbourne on the 1st ultimo.
12th March, 1889.
5) This lead me to:
Name: Mary Ann Sheehan
Spouse Name: William Titley
Marriage Date: 02 May 1885
Marriage Place: Queensland
6) So yes, William deserted his wife Mary Ann & daughter Mary Louisa, moved to WA, assumed the name of William Bell, and married my g-grandmother Louisa Florence Riley. No one in his WA family knew that Bell was an assumed name, until they went through his papers after his death in 1933. He was buried under his original & legal surname of Titley. (I gather the Bell women all felt like disowning him, after discovering the WA marriage was bigamous)
Leigh