i dont understand

It might be worth getting the car back and getting it repaired privately rather than take the write off money.

Our car was written off once when someone went into the side of it at speed, shunting it into a concrete bollard. It was so lucky that DH was in the on his own, as a passenger could have been a goner. The other driver was totally at fault, and ended up having to go to driver re-education classes. But a few weeks after the crash, we had a letter from her ambulance-chasing lawyer trying to put the blame at DH's door and claiming that the other driver and her three passengers all had injuries that they needed compensation for.

The position of the cars would probably have given the lie to the, well, lies anyway, and our insurance company dealt with everything. But the fact that two drivers had stopped at the scene and given their details in case he needed a witness helped enormously. We've said we'll do the same if we ever come across a similar situation.

Someone went into the back of us once; we exchanged details and the damage didn't seem too bad until we went to open the boot to get out suitcases out at the end of our journey and couldn't open the boot.

We immediately informed the insurance company and, as far as I remember, everything went through quite smoothly.

There is no point in paying insurance if they will not sort it out properly if an accident occurs, so I would get back on to them, keep a log of conversations and if necessary speak to someone higher up in the company and tell them you are not satisfied and will be taking it further if your DD does not receive a satisfactory outcome.

Has she got whiplash? If so, she needs to see the GP and get it diagnosed and she may be entitled to compensation.

The car will be deemed a write-off if the cost of repair is more than the value of the vehicle.

You could also speak to the CAB(Citizen's Advice Bureau). Therwillbe a local one and they do not charge.

Insurance companies seem to be loathe to investigate claims properly these days, especially if there are no witnesses. I was involved in an accident where a man jumped a red light and ran into me as I was turning right. To my mind, there was no ambiguity about it. There were two lanes of traffic. The car at the side of him stopped at the light and he didn't. By the time we got the vehicles into a position where we were not blocking the road, all the traffic had moved on, so anyone who might have seen the incident had gone. The insurance company insisted on dealing with the claim on a fifty fifty basis and I lost my no claims bonus. I was livid. They didn't get my business the following year. There is now a camera at those lights and not before time. I agree with twice if you are not happy tell your insurance company that your are contacting the ombudsman.

Your daughter needs to see a solicitor as she has been injured. These injuries could cause ongoing problems and she is entitled to claim damages. She also needs to see her GP and keep a diary of what happens. She can claim the costs if any treatment incurred.
Go to a reputable solicitor.

If your daughter is paying by direct debit for insurance, yes the insurance Company will take any insurance owed for the rest of the year from any settlement. If she had paid in full when insurance was due they wouldn't have paid her money back. You pay a year's insurance to cover for any accidents so the money is still owed to them - this happened to me took a little time to understand but does actually make sense now. What would have happened if the accident had occurred just after renewal date-would you expect them to sort out without having received any money. If your daughter wasn't at fault her insurance company will recoup write off value from other parties insurance but your daughters insurance cover is not the other parties responsibility

Someone went into the back of me at one point and my car was said to be unrepairable because the boot had been damaged and the metal had "pleated" and it would cost more to do all the repairs ( this was difficult to repair and would take a lot of time) than the car was worth. When your daughter gets a new car I would have thought the insurance company would transfer the insurance to the new car with an adjustment if it is a different make/engine size etc. My insurance company did this when I changed cars whilst the previous insurance was still valid. If someone goes into the back of you it is their fault not yours and yes I would expect your insurance company to claim from the other persons insurance on your daughters behalf. If you are unhappy I would complain, there are ombudsman to consult if you are not happy or it can't be resolved