Thank you for the additional detailed information, what a nightmare you are going through!
You have hit the nail right on the head with the fact that a limited guarantee corporation does not need to be transparent to its clients, only its shareholders, however it does need to comply with all the provisions of the Corporations and in this instance, the Trade Practices Act so the answer to your question as to how to sue them will be more along the lines on what grounds could you sue them for, and if successful, what damages would remedy the claim you would have against them.
Its not my place to determine whether or not they have misrepresented you in any way, which for me is a starting point under the Trade Practices Act, misrepresentation of what you expected to get for the fees paid - the license to practice here in Australia.
I believe you will struggle to get any court to hear about their unfair policies, it is material to the result but not enough to commence an action on.
Someone (a Govt entity) gave the ADC the right to issue these licenses, I would find out the source of the power they have and vent your discontent to this department and contact the local minister under whose portfolio the ADC would run under.
I would also suggest that you contact the state based law society to be referred to a Solicitor who practices in the area of the Trade Practices Act and see if there is a chance for you to pursue ADC for damages in this area.
I trust this information is of assistance and that you will kindly accept my answer as I wish you the best in this matter