Consider getting a lawyer
So your insurer is on the hook for replacing your car even if you are at fault. But they would like to settle with the other insurer such that the other insurer pays for their responsibility. They have no interest in making the other insurer pay beyond that, as you would get that money, not them. Your interests do not align here.
If the other driver is clearly at fault, talk to a lawyer. The lawyer gets paid a commission on the settlement. If you cut a deal with the lawyer where the lawyer only gets paid commission above a net $26,000 gain by you (compensation for your car minus any compensation you pay for the other car), then your interests will more directly align.
There is no reason you shouldn't get the replacement cost of the car here plus the lawyer's fees. And your insurer should still get their costs covered. And your rates should not go up. Or you should get more of a settlement to cover the increase in your insurance. And it is generally the case that lawyers don't charge for consultations in these cases. So offer the deal. If the lawyer wants to proceed, you have a good case. If not, then there may be facts not evident to me, and you can quietly continue your insurer negotiations.
Mechanically, the problem with the car is twofold.
- Hidden damage. Not all damage is obvious. Some may not become obvious for years.
- Unfixable damage. Some damage does not prevent the car from being driven but does cause problems.
Replacing the car handles both of those problems. Fixing the car leaves both of them.
To give you an example of what I mean, my mechanic also operates tow trucks (for other garages, dealers, police, etc.) and does body work (as well as mechanical work). He does not do frame work himself, but he has a long time personal friend who does. In general, he is about as informed a consumer of accident repair as you can find.
One of the tow trucks was hit by a car. It was sitting at a stop sign. A car broadsided the truck. There was no question of the truck's driver being at fault. Anyway, he repaired the truck. But after that, the tires always wore more quickly. But he didn't get compensated for that. He was only paid for the cost of fixing the truck, not for the remaining damage.
Your car is gone. If they repair it, you'll essentially get a different car that shares some of the characteristics of your old car. But it will also get weird new problems that they'll never get exactly right:
- Perhaps the frame won't align correctly. Particularly if something is slightly bent or twisted in the front of the car.
- Some pieces that come whole from the factory may be repaired rather than replaced with original parts. This is particularly true of pieces that run from the front of the car to the back, like brake lines. The repairs may be more subject to failure than the original parts.
- The wiring may never quite work right. Because they will probably splice it rather than replace the whole thing. And either the splice fails or they make a mistake in how they splice.
And of course I don't know everything that could go wrong. These are just examples. You may experience none of these and instead see some other problem.
Now, perhaps it would make sense for you to pay, say $18,500, for the repaired version of this car after collecting $26,500 from it being totaled. It might make sense then, as you'd have $8000 of compensation to pay for these problems. But don't think that the car you get for $16,500 of repairs is the equal of the car before the accident. It almost certainly won't be, even if you can't see the damage at first.
It is not at all strange for an insurance company to take a month to decide. That's perfectly normal and just how they operate. It may seem silly, as they are paying for your rental and may be paying storage. But compare that to the cost of hiring more adjusters and other employees. They are designed to always be a little too busy for the employees they have.