Depending on where you live leaving the dog in the car may or may not be illegal. This varies greatly from county to county, city to city, etc. Also the climate makes a big difference. Cars are like little overs / fridges and have extremes of temperature, even with the windows cracked. Depending on your geography, the dog's life could be in danger staying in the car. (Or the dog could happily be chilling out and used to this life style, it depends.) You could put in a call to your local police non-emergency line and/or your animal control department and talk to them. They'd be able to give you guidance about the laws of your municipality. It is true though, most animal "shelters" in the US (not all, but the majority) are kill shelters. So your mom's feedback is valid as well. Good luck!