Couple of problems. First is you shop doesn't total your car, the insurance adjuster does. They are all about least expensive way out. There has to be some critical damage (bent frame/major engine/major safety) that costs more to fix than write off before they total a car. Age is a factor, too. Second, were any pictures taken at the accident? If you have minor damage photos at the accident site and major damage later you've got problems.
If they fix it make sure you've got full coverage and park it in a bad neighborhood one night during a Jewish Lightning storm. (I've always heard it called Jewish Lightning)
