Although I am even more confused by your update I will say that I think your cousin is guilty of theft. Not by getting a discount but if he indeed charged his room, calls or purchases to your credit card that is theft.
You still haven't said if you plan to call the cc'd company, I can't help but wonder why. I would call and write to the cc's company and make sure that you dispute those charges. Regardless of AP's AKL, and relatives you were charged without your consent.
Your cousin used your credit card, that is fraud, and AKL made the charges however the person who has to pay the cc'd card bill is you. If you don't dispute the charges then you will have no recourse if your cousin dosen't pay you. IMHO AKL dosen't owe you anything but your cousin certainly does. AKL does have the responsiblity of proving how and why the charges were made to your card and if it turns out your cousin signed something he should not have then he will have to pay the consequences.
Good luck
TJ