If you're a divorced parent of a teen driver, you need to work out the issue of whether your child will be on your car insurance policy or that of your ex, or both. The answer of whose policy (or policies) your child should be covered on will depend on a number of factors, including whose vehicle(s) your teen will be driving. Whatever the case, this is not an area where any residual animosity that you and your ex have towards each other should get in the way.
The most important thing is to make sure that your teen driver has proper insurance coverage. If not, the results could be financially disastrous. It's essential to discuss this with your insurance agent. You should be talking to your agent about getting your own insurance policy once you work out who is getting which vehicle(s) in the divorce.