This will depend on the state ( if in the US) each state has different rules on car insurance. Often at least in GA and TN, if the underage driver is insured on one car in the family they are insured on all of them, since they are a listed driver with that company.
At least in the states I am a agent in, any licensed driver is covered under another policy unless specificly limited from it. or unless the policy only insures those listed drivers.
For example, If I came for a visit and you let me use your car, I am covered under your policy to drive the car. I can let people I know, friends, co-workers all use my car and they are all covered.
The issue with a underage driver living in your household, that they have to be listed as a driver in your household with your insurance company.