To clarify:
If somebody is on your policy as occasional driver then no matter how many accidents the insurance will pay.
If somebody like your kid is not on your policy, he/she can drive your cars and insurance will pay first time. But be careful! Your are taking insurance's advantage and insurance will not pay the second time.
You better list your kids as occasional driver if he/she quarlifies (for example, full time student away from home more than 1,000 miles). Premium for occasional driver is not particularly expensive even for a young driver.
Clarification: You need to pay primium to be an occasional driver though his/her name does not necessarily have to be on your policy.