在我们州 ( 非CA), 州法规定保险公司自动COVER小孩, 除非你EXCLUDE你小孩。有的保险公司不让你EXCLUDE除非你小孩有其它的保险。
In your case, if you were in our state and you did not exclude your child clearly ( assuming that insurance company allows you to do so), your child actually had insurance since the insurance company would have to pay if your child had an accident during the past two years.
So I think you should check your state law first.