Is it permissible to return to Australia if my presence there is better for my religious and worldly affairs, knowing that I relapsed after returning to my home country, and no longer find the religious atmosphere that was there?

If the parents permit travel to non-Islamic countries, then there is no harm, especially if it is better for one's steadfastness and da'wah activities, provided that the conditions for a Muslim's travel and residence in the lands of the disbelievers are met. These conditions are: possessing knowledge to repel doubts, having the faith that prevents one from succumbing to desires, and there being a need for that travel.