If you believe your insurance company is not properly investigating, you should hire counsel to represent you. Although counsel for the insurance company will likely be hired for you if this matter goes into litigation, it can sometimes be unclear where the attorney's primary interests are - protect the client or the insurance company?
But to answer your question, your insurance should absolutely fight this, especially if the facts are what you allege they are. For now, get copies of any police reports and speak with the adjuster handling the claim regarding the status of the case. Your insurance company is probably in the process of investigating. If the insurance still claims it's your fault down the line, get your own counsel to fight it if your exposure is high.
Side note: Have you interviewed the driver of the SUV to see if they can recall getting hit twice?
The facts of the case are in dispute. However, in most rear-end accident cases, the vehicle in the rear is deemed to be a liable party. The issue would be dependent on the actual sequence of events. You may have partial liability for the second impact of the first vehicle and you also may have partial liability for the impact to the vehicle in front of yours.
You are at fault for rear ending the Mustang. However your insurance carrier should defend you against the claim of the SUV. Check with your insurance carrier for the proper appeal process. the facts you describe regarding the various vehicle damage strongly support your version.
As the car accident attorneys have explained, the fact of the matter is that you are liable for hitting the car in front of you. Consult with a motor vehicle accident lawyer if you believe otherwise. Best of luck.
while there may be some "comparative negligence" on your part, the mustang operator clearly shares in that fault. Depending on the laws of your state will determine how much your insurer has to contribute to the accident. Your insurer absolutely can and should fight this. I would tell them you are ONLY responsible for the damage to the rear of the mustang and a percentage of the front damage. If either of the drivers (or passengers) of the vehicles in front of you bring a lawsuit against you, your insurance company will bring in an attorney to defend you. Keep in contact with your insurance adjuster. Great question, we see this type of thing quite often, actually.
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