What will happen to our car insurance rate?

16 yr old son got his license. Wife and I have 2 fairly nice cars. Full coverage. When we added my son our rate doubled, more than doubled actually. His grandmother is giving him a car this week. Not worthy of full coverage. How should we handle the insurance. Can we list him as primary driver on that car and do liability only? Will that make the rate go down or will it go up even more?