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

I hired XXXX XXXX XXXX to install a custom wine cellar in my home. 
In his contract there is a final payment that is to be made after completion of the project. As we stand today XX/XX/XXXX this contractor has not completed the project. The refrigeration is not installed and is not even on site. His installation person, XXXX, damaged the wine cellar door by drilling the hole incorrectly. He then compounded it by trying to force the lock into the crooked hole resulting in a damaged lock. 
I contacted XXXX XXXX and explained the issue and asked him if he would like to return and correct the issue or would he like me to contact the locksmith to see if he could fix the lock and correctly install the lock. He instructed me to call the locksmith. I told him that he was responsible for the repair and that if he could get some stain it will be needed to repair the door. He told me that there would be a half of a pint of stain in the cellar. I told him that there was none and I double checked with another person. He said that he would order some. I called several times to inquire and after a month I called my cabinet finisher to see if he could stain the door and hide the damage after I asked my cabinet person to try and fill the hole that was left when the installed decided to drill half of the hole from each side and the holes did not line up straight. I have not received the cabinet persons bill yet and I have only received the bill for the outside of the door. It looks funny as it is two different shades so the rest of the door will have to be stained to insure uniformity. 
What I learned when I examined my statement was that XXXX XXXX fraudulently charged my credit card for the final payment upon completion which I not only did not authorize, but I told him that he could not charge the card for any amount that I did not sign off on. He did this to avoid responsibility for his peoples damage to the installation. 
There are other damage issues that need to be paid for as listed below : 1. XXXX inspected and monitored the installation of the cellar himself including the placement of the foam insulation which ws placed after the conduit was run for the electrical light switches and the thermostat. When his installers showed up they installed right over the switchboxes which meant that the walls had to be opened and the thermostat and light switches ahd to be moved to a new location. This included costs for the electrician, the drywall people and the painter as well as the cabinet maker having to modify the cabinetry to accept the thermostat and the light switches. The electrician and the drywall change costs were {$450.00} per my contractor XXXX. 
2. The cabinet costs associated with this will not be clear until cabinet person gives me his final bill.

3. The locksmith charged me {$150.00} to un-bend the lock and straighten he home on XX/XX/XXXX, which is the day that I called XXXX and told him the charge and he them with out my knowledge or authorization charged my credit card for the {$1800.00}. 
4. The Cabinet finishing person finished the door outside but not inside the jamb or on the inside of the door and it looks funny so the entire door needs to match. The first part of the cost was, {$450.00} and the rest of the door will cost an additional {$350.00} and will be completed next week.

I am trying to be reasonable. I am not responsible for the damage that his contractor created. I offered XXXX XXXX XXXX  the opportunity to return and fix the issue or offered to have it done. They have not responded to me since they charged my credit card which is totally not acceptable. 
This vendor acknowledges that he was aware of the damage. He acknowledges that I would not give him authorization to use my credit card for the entire payment of this project by altering his bills to write the amount that was acceptable for the work performed at various agreed upon points. When there was a problem he used the number from a previouis charge without my knowledge or authorization. He never attempted to remedy any of the issues that he was responsible for. 
He does not have the right to take my credit card and charge it without my authorization or knowledge. This is fraud. 
Respectfully, XXXX XXXX