since it was an add on card. the primary card holder shall be sole responsible for any wrong doings of the secondary card holder. Thus, while issuing add on card in the relation you need to be very careful as th person may misuse it or may cause problem and you might not be in a position say much.
Further, you may not take any legal action except recovery of dues, if any. Since you were aware that if the said person doesnot settle the dues of CC on time then it shall affect your credit rating. Therefore, you cannot take any action for drop in rating.
Advocate Rohit Dalmia