My blog from two days ago answers all of your property damage questions here. Www.ryanmontgomerylaw.com/blog see the low ball offer blog.
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It is no unusual to have a dispute as to how much rental car time the at fault insurance carrier is responsible for. From their perspective, the offer they made on the car is reasonable, should be accepted, and should therefore cut off the obligation for ongoing rental. From your perspective, they should continue to pay for a rental until they make a fair offer. It should be noted that under the law, they are responsible for paying fair market value for the car whether that allows your daughter to get a replacement car or not. That may not be fair, but the obligation to pay for a rental will stop soon after a fair offer for the car is made.
Since your daughter was hurt, she should probably consult a good personal injury attorney who will represent her on a contingency basis (no money up front required) and will likely help her deal with property damage issues.
Consult with an attorney. Most attorneys will not charge you anything to consult with you on a carwreck case.
My family and I were in a bad car wreck in November. A drunk driver turn in front of us on a 2 lane road. I hit him doing 50 mph. I have represented many people who have been injured in car accidents. The wreck gave me a very different view of how it works. It was amazing how nice the first adjuster was to me. That changes when you try to get what you are entitled to. Long story short, you can usually make them repay you for the car rental when it goes over (at least progressive did for me 3 months later), but don't settle anything until you talk to a lawyer. I would be happy to speak to you or contact a good attorney in your area. Like I said most will only charge you a percentage of what they recover.