Complaint sub-issue: Credit card company isn't resolving a dispute about a purchase on your statement

My XXXXyear-old, XXXX XXXX, child made over 20 purchases in the app XXXX XXXX with my boyfriends credit card, I am an authorized user on the account. These purchases were not authorized, and I had no knowledge of them. When I reached out to the XXXX company through their support link, I was informed that I am responsible for the purchases no matter who made them per their policy. I again reached out and asked for them to look further into the matter because I havent even played the game in several years up until recently and that is when all the charges started occurring. These charges are fraudulent in the fact that a minor made them without my consent. I have put all the necessary safeguards into place since finding these purchases. I have removed the app, as well as changed all necessary passwords. I have also deleted all credit cards from my XXXX XXXX  account and locked the physical cards in a safe. I have since filed a complaint with the BBB as well as emailed the " support '' for the game a second time. These charges started in mid XX/XX/2019 and continued daily until XX/XX/XXXX. 
The response received was : " Hi XXXX, We are sorry to hear about the situation you encountered. Normally, we would have been able to assist you with refunding the unauthorized purchases, however, in this case, the transactions were also used in the game which will not allow us to retrieve the purchased goods and trigger the refund mechanism. We strongly urge you to set up parental control on your devices as it is out of our control if someone underage is accessing your account. As per our Terms of Service, no minor should be accessing the game, however, we can not monitor or prevent minors from accessing accounts owned by adults. It will help you tremendously to avoid this kind of situation in the future if you set up your devices in a way that will prevent your child from accessing the game and purchase. As a less effective method, you can also remove the card details from your accounts so the purchases won't go through even if there is an attempt at purchasing by someone other than you. I am sorry I was not able to help more this time, but I hope the above pieces of information will help you going forward. Best regards, XXXX XXXX Customer Support Manager XXXX XXXX Support '' I emailed the company back the same day and informed them that these were not authorized purchases and that there was no physical item received and to please just close whatever account is associated with me. To this date I have not received a response from the company on either the BBB complaint or the personal email. 
I have also contacted a pro-bono lawyer in my area. One credit card ( XXXX ) account has refunded some of the purchases but not all and the other ( Sears Mastercard ) refuses without me filing fraud charges against my daughter. I have explained to Sears that my daughter is XXXX XXXX and did not do this knowingly. XXXX has mislead me a few times in that the first time I called, I was told that " we could file the dispute but if the company said the items were received then that would be the end of it. '' It was also suggested that I attempt to reach out to the XXXX company again to see if they would be willing to work with me at all ( referenced above ). The second time I called XXXX was after I had done some researching on the FTC website and came to the understanding that it is federally illegal to be held responsible for charges that were not authorized. I spoke with another agent in the dispute department of Sears and was told I needed to email all the information and supporting documents to XXXX. I did and received an email back asking for a dispute claim number and that if I didn't have it available to contact customer service to get it. This phone call led to me being forwarded to the fraud department at which point the representative informed me that unless I were to file charges against my daughter than they would not be able to process the purchases as fraud. 
The total amount charged to my Sears Master card is {$4900.00} to date I have been credited ( through XXXX and XXXX XXXX requests ) {$1000.00} leaving a total loss of {$3900.00}. I am accruing interest on these purchases and my minimum payment has gone from {$52.00} on XX/XX/2019 statement to {$190.00} on XXXX statement. 
I have received free legal advice to file this complaint on this forum as well as to see where the complaint with the Office of Attorney General against XXXX XXXX goes. I am seeking a full refund of all unauthorized purchases. These purchases start on XX/XX/19 and continue to XXXX and are made to XXXX XXXX, XXXX XXXX or XXXX.