Full details for the birth and death of Maud - where was she born and died (at home, in an institution or hospital?), would be extremely useful.
I see on Trove that in 1877 and in 1880, a Thomas Minton was advertising in Sydney newspapers saying he would not be held responsible for any debts incurred by his wife. The first date lines up with the kids being in Randwick, perhaps she'd left the family, and the children were temporarily put into care as a result, with their father then fetching them out when he was able.
Given this, and the gap between kids, we can't be sure that she didn't simply put down Thomas as the father on the certificate even if they were living separately at the time, for example. And she could have easily gone back to using "Murphy" or switched to another name altogether, which will make her hard to track.