Ready Mix Concrete Company Sprayed My Truck W/ Concrete

Preface, I do have an attorney but am still seeking advice from internet randos on a Sunday afternoon.
Last November I bought a brand new truck (2024 model), then in mid December I was driving down the highway to work when a concrete truck going the other direction was spraying concrete out the back like a fountain while doing 55 mph down the road.
Several cars following it were damaged, my truck was covered in concrete, the windshield was covered and severely pitted, the paint was chipped, the headlights pitted, chrome chipped, concrete stuck to the plastic parts and doesn't come off.
The concrete company readily admitted liability but stated their policy was that I had to let their chosen companies fix the damage. They would pay direct, not thru insurance. I took it to their company for an estimate but they wouldn't put in writing what they would do or the cost. They also wanted to use non GM parts and an aftermarket windshield.
I took it to 2 additional shops for estimates, one well known local shop estimated the damages at $11,700, and then I took it to the body shop of the GM dealership where I had just purchased it and they estimated the damages at $12,500.
After months of delays and back and forth they finally agreed to pay the amount of the GM dealer's estimate. They then sent me a check but made the check to the dealership/body shop.
It seems to me that I'm the one who sustained damages and should be reimbursed. I have a real problem with someone who caused me $13,000 in damages dictating the terms of how they'll pay for the damages. It's also an issue because as a small business owner I can't really be without my truck. I just want reimbursed for the damages they caused.
Furthermore I haven't asked for anything for the weekend I spent cleaning the truck, or a rental for when it's repaired,, or time getting estimates, or the countless hours I;ve spent on the phone and emails with them, and now having to pay for a lawyer.
Am I wrong in thinking I'm entitled to be written a check for the damages and then it's my right to proceed how and when I want?
Any suggestions?
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