Can I sue a company if their company vehicle injured me and totaled my car?

I was rear ended at a red light by a woman driving a company owned vehicle. She didn’t have a valid license and is the wife of the owner. She was driving around with her child in the back of the vehicle. She ended up totaling my new (to me) 2010 Mini Cooper S and potentially causing permanent injuries to my spine. Officer on scene cited her for driving without a license, but she gave him false information, eventually tracked down who owned the vehicle, it ended up belonging to her husband’s carpeting company. Can I sue said company for this even though they have insurance? The insurance company doesn’t want to pay anywhere near what I paid for the car two weeks ago.