This is something I probably should already know about, but didn't, so thank you! Is it generally a separate claim than the accident claim and at what point is the diminished value claim filed? Now, or after the repairs are finished?
Here in Virginia, it is not an entirely separate claim, and I don't think it would be in other states. You are just pointing out to the claims adjustor further "damage" that you have sustained as a result of the accident. The adjustor isn't just going to volunteer to pay it, he hopes you know nothing about it, you need to ask for it.
Tell the adjustor that you know that when you go to trade in your vehicle, they will pull the report that shows structural damage, and it will state exactly on the report that "structural damage may impact vehicle safety and reliability”, and as a result no dealer is going to give you the same amount for trade in than if this wasn't on the report, and it's the fault of "their insured" that this is now on the report. The more he knows you know, the less likely he/she will try to get around it. This isn't like a "pain and suffering" type of loss that is often used to pad the figures as a scam. Your vehicle is now worth less, even after repairs, than it was prior to their insured having rearended you, it is a real financial loss to you which was of no fault of your own.
It isn't damage the insurance company is likely to cover without a fuss. That is why I said if it has frame or structural damage, then you should definitely ask for this part to be covered, as your vehicle will have more of a diminished value than simply removing a dent or scratch out of a door or bumper which wouldn't be worth the effort. You may have to "squeak" a bit to get it covered, so don't take no for an answer the first time, but be friendly about it. People want to help someone who is being friendly much more than they want to help someone who just lit into them. There may come time for that as well, but try friendly for awhile. Please let me know if it worked out for you, I'm curious.