preliminary estimate

The other party's insurance company will right me a check if I so choose but only for the amount of the preliminary estimate on damages on my car. I'm not happy over the preliminary estimate.The insurance's auto body shop did a 3 to 5 minute check up.Came up with around $1700, then the insurance called me and said the auto shop gave them a discount that went down to 1500. Ins. Co. did not accept an estimate I got on the very day of the accident from an independent auto body shop.
What are my rights? What can I ask for under the law? Can I ask the Ins.Co. to do another estimate. But they are always seeking to go as low as they can for compensation. How can I get the most of them?Thank you.

P.S. : What hurts most about accidents is not the actual accident but what insurance companies do to the victims afterwards.Somehow we feel cheated and laughed at.

you can always pay a body shop to do a detailed exam of your vehicle and write up a more thorough estimate. some shops will waive the cost of that exam if you let them do the work on the car.

If the other carrier doesnt want to pay the estimate you present, you can always take the other driver to small claims court for the property damage. once you get a judgment, the other carrier will have to pay the amount.