My question involves a consumer law issue in the State of: Kentucky

I took my car into a repair shop (by appointment) to have both rear brake lines replaced. Upon installing the new brake line, they somehow managed to strip the threads of the ABS module. This resulted in me needing a new ABS module. After I told them I refused to pay for a new one, which is over $400, they claimed they could get a used one for around $75. But the other issue here is that I brought the vehicle in before the shop opened up that day and the job was estimated to take 3.5 hours to complete. After about 5 hours they told me they had to STOP working on the car so that they could work on other cars. This resulted in me being without a car because they stopped working on it. I had to rent a vehicle for two days. I can't really prove that their negligence caused the ABS module to be damaged other than a peculiar chain of events:

The only way I could prove this is by the order that things occurred: The mechanic shop told me the threads were stripped AFTER they ran the new line, suggesting that it happened when they were inserting the bolt only AFTER the new line was ran. They did not inform me the thread was stripped immediately after removing the bolt even though they said they saw "pieces of aluminum" on the threads of the fitting after removing it. I asked them if they cross-threaded the fitting when inserting it into the ABS module, and they went on about the car was "full of rust" on the frame, which had nothing to do with the ABS module itself. And the threads in the ABS module were aluminum which does not rust. Another mechanic I spoke to claimed that he was almost certain they cross-threaded the fitting.

My main question is this an insurance claim against the mechanic shop for negligence, or should I make a claim on my insurance policy since the mechanic's mistake (and refusal to finish the job the same day) caused loss of use of the vehicle?

I was charged the $75 for the replacement ABS module but not for the labor of removing it and installing the replacement. My auto insurance has rental coverage but only if a claim is made.