procedures: double citizenship with the US UU and Australia, but with only a US passport. UU

Probably not. As Australian citizens, their children are not eligible to receive ETA, and they will not be allowed to travel on the plane without one. If you arrive at the border with Australia, there may be some problems while things are resolved, and more problems if you leave the country without an Australian passport (although you can request one while you are in the country to avoid this).

Having said that, some people have reported that they request ETA as Americans and that (incorrectly) they have been granted one anyway, so their mileage may vary.