The question of provate sale price or garage would depend on how you purchased. It should be like for like. On the basis of price if it was lower thn market value the ins. company will assume that is due to condition.

Cat D sounds like quite a bit of damage.

Parts are expensive, even pattern parts, labour costs are probably £35 in a back street body shop & considerably more elsewhere.

Add to that car hire charges for a week (even modest repairs require drying time / several coats, rubbing down and working in the colour to match the old paint, admin costs @ Insurers etc etc so a small bang maybe £1000 - £500 repair, £200 car hire + delays in parts and the costs rise so many cars are written off to avoid the risk of cost overruns.

Back Street Body Builder using pattern & 2nd hand parts and having lower overheads can have a £800 repair down to maybe £100 parts and £250 labour - can still be a good job BUT if the car is CAT D it can devalue a fairly new car- by the time the car is a banger age it makes little difference as at that point overall condition is key.

Airbags deployed? most 5 year old cars ( & some even newer) will be written off as uneconomic

"If we take the offer, buy it back, have the work done we could be around £1k better off, but I suspect that the insurance will go up, and the resale value will be less, so probably worse off in the long run."

Possibly not. If you run the car till it dies, the resale value is irrelevant.

You "suspect" the insurance will go up, but unless you know by how much, you cannot be sure you'll be worse off in the end.

Higher up you say the insurance company has "...offered us a figure which is just less than we paid for it. Fair enough she has had a few weeks driving it, and has added a few miles, but we cannot find an equivalent car for the amount they are offering. There just aren't any for sale for the price."

I think this is the option I would take. You need to get rid of the sentimental value that it seems has been attached to the car - "the perfect car", as you call it. Call me cynical if you wish, but I simply don't believe that there isn't another suitable car out there. It doesn't have to be the same make and model. And it won't be the last car your daughter buys.

You've been made a good offer - the use of a car for 8 weeks free.

But you make a fair point that "it doesn't seem fair that she is the person suffering through no fault of her own." Indeed - she is the victim, but unfortunately no-one gets compensated for all the time and effort they spent searching for the car.