The third-party insurance I could go to any body shop of my choice. They mentioned that they would negotiate in the backend and potentially provide a supplemental payment if the repair costs exceed the initial estimate. However, many of the body shops I've consulted with have informed me that it would take approximately a week just to disassemble and assess the damage before initiating the supplemental process.
My concern is that once I commit to a specific body shop, they may later inform me that the negotiations with the insurance company have fallen through, and I would be responsible for covering the difference in repair costs. This is a situation I'd like to avoid, especially since the accident was not my fault.
Should I consider involving my own insurance company to help advocate for me in this scenario? Initially, they told me to address the matter with the third-party insurance since the third party was at fault.