Hi Mary and Kellie
Yes there were 2 children were born in NSW, Mildred and Elsie.
You need to be aware there are 2 Walter Bye's and the child Lottah was born to the "other" Walter Bye. Walter Bye the father of Mildred did die in 1953.
Mr William Bye of Perth was the father of Walter Bye (father of Mildred). The other Walter Bye was the son of a brother of William (hence the similar timeline for birth of the children).
I don't know of the James Smith of Turners Marsh that you mention and will need to check this out further.
Let me know if any of this isn't clear.
Thanks for your time,