I'm so sorry to hear about your wife and daughter's accident, but am glad to hear that they are not seriously injured.
Dimunition of value is absolutely a valid claim in an auto accident, and understandably the other person's insurance company won't offer it to you in settlement. It is absolutely something you can pursue. Laws vary across states, but in Alabama, you can recover as long as you aren't at fault.
It is possible to recover for emotional damages/pain and suffering in a car accident. Depending on the long term effects on your daughter, it is possible that you can recover.
I would recommend contacting a personal injury attorney - most offer free consultation and many work on a contingency fee. This will help you make sure you meet all deadlines, etc. You can also obtain an offer from the insurance company, and then work with an attorney for a contingency of what the attorney recovers for you ABOVE the amount of the original offer.
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