I understand that. In NJ our young drivers are a bit older and our own kids waited till about 18 to get serious about driving. When our youngest went to college in the snowy mountains of Pennsylvania, she did not have a car for the first year. Then we found a used Subaru for her. Then she hit a deer. Then she hit another deer, and that's the deer that did it in. Then we helped her buy a 2017 Subaru with Eyesight and all the bells and whistles Subaru can load on.
We love our old Grannymobiles, but it's true that newer cars have lots more safety features and more protection for the driver and passengers.
Sell the old Avalon and get something nice and new (and safer) for yourself!