Etienne: I am not sure I know the solution for your problem.
Malaysia is rather commonly regarded as a common law country where implementation of the law is a problem.
A fair starting point is that you are not responsible for your father's unfortunate poor financial condition. Go through the credit card's terms and conditions to determine whether the supplementary card was issued where the principal cardholder and the supplementary cardholder were both joint liable for its usage. I suspect this is so. Even if my suspicion is right, you still would be available to justify by your age and your financial reliance on your father as your defences.
It is good to get evidence that the bank refusal of granting you a credit card was basing on your father's supplementary card matter in the past. In many common law countries, such refusal would be shot down promptly. These countries tend to have legislations like Bill of Right Act in protection of human rights; Ombusman Act to free and easy access to the public against the public and private sectors; Privacy Act that enable individual to get access to the information that organisation holding on the individual and the right to reply for the individual. The bank in providing a "public service" role is not allowed to make its discretion using irrelevant consideration [default in your father's credit card account would likely be fitted in].
In practical sense, I suppose you may bring your case to Bank Negara which is supervisory body on banking and also covering many financial services. The general point is to get your facts right. Having a letter from the card issuer stating the reason for their refusal is great, but not essential. You may put the facts to the card issuer and their failure in rebuttal may support your contention, on the balance of probability. After you have failed to settle the matter with the card issuer, then bring it up to Bank Negara. There seems to be some standard complaint forms available from the banks or Bank Negara website that would guide you in your complaint.
