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It is not the use of the vehicle to go back and forth to work that made your vehicle commercial and requiring a commercial insurance rider. What makes your vehicle commercial and related to your business would be the fact you had your company name on the vehicle I am afraid. You need to read your policy
to see what it said about commercial use, but if the truck was at your home and not on a job, then you do have grounds to argue as you state above that it was not being used at the time of the theft for any commercial purposes. You need to start by sending them a letter informing them that the car was parked in front of your residence, which is listed on the policy and was not being used for any commercial purpose at the time of the theft and their denial of your claim is bad faith based on this reason. However, if they will not pay still and depending on the exact wording of your policy about commercial use, you would then have to sue them in court for breach of your insurance contract
to obtain payment out of them.
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