Been a while since you have had a car repaired. The parts alone are over 2k. Unless you are in the business of repairng cars don't give spurious advice about how much it will cost.You will be surprised.
However, I do assure you a good clip can be had for that vehicle for well under $1500. So, what will happen to Alouette's car is that it will be sold as salvage for $500, The rebuilder will buy recycled parts, 'cut to size, beat to fit, and paint to match,' and put it on the lot. All told, take him a week. He'll try to make $3,000 more than his cash investment, but take anything close. Done every day in your town. If he knows his business, it will be a good-looking serviceable vehicle.
In regard to the car/title controversy. Yes, it does vary from state to state. But, you are definitely "allowed" to negotiate the damage as distinct fom the vehicle. There is no reason for an insurance company to "buy" your wrecked car, except their convenience and financial model. OTOH, they're allowed to try and to mitigate their underwriting loss by "buying" and then selling that car.
I have personally asked for the money AND the car on behalf of many friends, and myself; and more often than not, made that deal. If Alouette really, really wants to keep that car, no reason not to try. OTOH, with that amount of money in her purse, she has many options.
But Rhiannon, I do realize that my advice is some times not entirely appropriate for folks like Alouette who are not hardened motorheads, or who don't care to learn the ropes in this part of the automotive jungle. So, somewhere between epow and myself, lies an answer for her.