If the adjuster's initial offer falls short of the estimates you collected, you should consider negotiating with the car insurance company. You don't need to file a lawsuit to get started. These discussions can take place in person or via email, but it's important to get the final decision in writing. Everything is negotiable, even if an appraiser won't admit it.
The insurance adjuster may try to get you to reduce your initial claim, but don't accept a lower offer until they increase their original offer. When negotiating, it's important to remember that you should never reduce your claim more than once until the other party increases their original offer. This will help ensure that you get the best possible settlement.