If your car gets into an accident, you have two options: your fault or not. If I'm wrong, you can get a rental car from your insurance company if you have rental car insurance.
If you are innocent, you can get a rental car after an accident that will help you in. Some state laws require insurance companies to pay the offending driver a "reasonable transportation fee" or a "reasonable replacement car rental fee" when repairing your damaged vehicle.
Most companies pay a fixed amount. However, if there are special circumstances that require a vehicle similar to your damaged one, report this to the insurance company to see if that cost is covered.
You need a car – so you'll be arguing about the same as yours, but you'll have to get back on the road soon. You have kids to take to soccer practice and have to go to work in the morning, so "staying basically" might not be the best approach. You have to choose your battle and now your main need is to get another phone.