Hi Myname2222
I agree with Sophea...
In Australia, a man's female live-in partner can be married or de facto (unmarried to him).
The 1961 Australian Marriage Act does not recognize polygamous unions (several wives, or de facto partners treated as wives for legal purposes).
Re your question, a man's wife would be considered the predominant partner due to formal & legally recognized marriage laws in Australia that allow only 1 wife. The live-in girlfriend would be considered similarly to a live-in tenant, or someone simply residing in the same house. Both women could legally have the man's children & their biological father would be responsible for child maintenance / support arrangements for all children in accordance with Australian laws.