Wow. I'm sorry to hear you are having a hard time, Mosman, but I am racking my brain to think what you are spending all that on. We are on less than half that, admittedly not in one of the most expensive suburbs, but a very nice cafe-strip "trendy" one, and are doing fine, with a much nicer place than we had in London, with a good sized garden. The kids both do weekly swimming lessons and other activities, and we spend max $500 a month on groceries, cleaning items etc, including lunches for DH. We don't receive any govt assistance or payments, although I am looking into whether we can get something similar to the UK Child Benefit.
There are some lovely leafy old suburbs like Mount Lawley, Wembley, inglewood, Mount Hawthorn, East Fremantle, (just off the top of my head) which would all be cheaper than Nedlands, have good schools and not involve a two hour commute. You know the private schools you mention are also the most expensive in Perth and not necessarily the best?
Sorry OP, don't mean to ignore you- don't feel that you need tonecessarily go for private schooling. Our local govt school is lovely and in fact one of the reasons we moved from London