Auto Insurance Claims: Insurance Claim, driver insurance, insurance claim


Question
I want to make sure that the insurance company pays all expenses before I leave my car to be fixed in the auto shop. In addition, If I'll decide to fix it I want to take it to my mechanic. The problem is that $200 not seems enough for repair. I asked the insurance to send me the estimate. What do you think should be my next step?
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The estimator from the auto shop that the other driver insurance company sent me to, told me that he will suggest replacing the bumper, however the insurance company of the at fault driver are willing to pay only $200. What shell I do?
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The text above is a follow-up to ...

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I was involved in a rear end accident were a cab driver hit my car's rear bumper. I took the car for an inspection in one of the shops from the list that the cab driver insurance company sent me. The inspector told me he will suggest to replace the bumper. Now the cab insurance company suggested me only $200 for repair. I know that it costs much more to repair it and to replace it far more..
If I just paint the bumper, after a while the paint will be cracked. What should I do??
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If the bumper is repaired and refinished properly, there is no reason for the paint to crack.
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Did neither the body shop or the insurance company explain the supplement process to you?  Does is not say anything about supplements on the estimate?   If the body shop needs anything addition that is not on the insurance company estimate, then it is their responsibility to contact the insurance company with the additional needed items.  The two of them will work it out.

Answer
What you are asking for is impossible.  No one knows exactly what it will cost to repair the vehicle until it is taken apart and fully inspected.  This is why the estimate is called an estimate.  There is no language on the estimate saying that no mare will be paid.  
If the body shop needs anything addition that is not on the insurance company estimate, then it is their responsibility to contact the insurance company with the additional needed items.  The two of them will work it out.
There is only one next step and that is to have the car torn down for a complete inspection and then allow the supplemental process to proceed between the shop and insurance company.