News to me Noel, and I grew up in the area. The swing bridge over the Maribyrnong River was replaced by the Dynon Bridge in the 1950's. Swing Bridge Motors, GMH dealer, was a landmark on the corner of Dynon Rd and Sims Street for many decades. Going by the description the track had to be off Sims Street somewhere between Dynon Road and the rail bridge that crosses the river tongue south and enters the tunnel under Bunbury Street. The only land with acreage to host a trotting track is along the river between these bridges. Now, it is all freight terminals and container storage.
The trotting track would only have been short lived. The whole Dudley Flats area was redeveloped during the 50's for rail and road freight. The illegal slums that gave the Flats their infamy were mainly at the West Melbourne end (according to my Dad). The standard gauge rail, from April 1962, used the Bunbury Street tunnel exclusively and the construction of Swanson Dock changed the entire area.
Further upstream, at the end of Doncaster Street Ascot Vale, Steadman's trotting track served trainers until the 80's when it was transformed into a golf course. I don't know what year it opened but it was in use from my earliest memories in the late 50's. It was never used for trials, though. Clarrie Allen, Tom's brother, and Albert "Darky" Gath and many others used the track. In those days the Showgrounds used to close for training around 9:30 and was never open on Sundays.
Sorry I can't shed more light on the Dudley Flats track Noel.