from your earlier information i think you've all gone through the mill, i do hope your husband gets better and he can enjoy OZ, but if its clear Adelaide had that feeling and Melbourne hasn't it speaks for itself. especially if your boys prefer Adelaide, it seems you will all be far happier in Adelaide, there are jobs but its a case of setting your mind away from what you specialize in to deeper and wider thinking, what you can do until you eventually get what you want. too many people emigrate and won't shift from changing their set career mind and end up going home blaming the country for limited work. that's what i find a joke.
you have clearly kept things going and kept strong through the difficult times in a different country and away from family so i think you can sort this issue out.
As a primary school teacher you will have many skills such as good management skills, organisation, good communication skills etc so they will be something out there for you.
hope things work out for you and your family