Deer smashed up my wife yaris....

So, on monday night a deer ran out infront of my wife on her drive home. The front of the car is banged up the front pretty bad but not past the point of fixing. Problem is that they want to total the car without even listing the cost to fix for us. I have asked for a list of costs and a full estimate and haven't heard back yet, but they are pushing to total it.

She loves this car and I think it can be fixed for way less than what would total the car. What should I do at this point? I didn't accept their first offer, and asked them to send me some more info about the break down of the repair. We have a rental for now, but took 3 times at the rental place to find a car that would work for us, so we can drag this out a bit.

Anyone have advice?