Why not get them e-visitor visas and then apply for 864 visa when they are in Oz (do it within 3 months as e-visitor only valid for 3 mnth stay). It worked for us.
Your mother would be issued with a BVA as soon as she applies for a 864, so she can wait in Oz. But she would have to apply and pay for a BVB is she wants to travel abroad and return.