Generally speaking, under Ohio law, an owner of a vehicle cannot be responsible for the damages caused by an adult driver of the vehicle except in two instances: 1. the driver is acting as an agent, employee, or servant of the owner (i.e., is running an errand at direction of owner, delivering goods at direction of owners, etc.), or 2. The owner has reason to know that the driver is not fit to operate an automobile, either because of a mental or physical impairment or disability (which includes under the influence of drugs/alcohol, no driver’s license, blindness, health condition, etc.).
If neither of these situations apply, then generally the owner of the vehicle cannot be held personally liable for the damages caused by the driver. So if your son would be in an accident that exceeds your insurance coverage, they could take an excess judgment against your son and his assets, but not your assets, so long as the two scenarios above do not apply.
If you are really concerned about your son driving your automobile, then you can either not let him drive it, or you could increase your insurance limits beyond the $1.3M in coverage you currently have. Though, to be honest, in most instances, you would have more than sufficient insurance, with the exception of a death resulting from the accident.
Best of luck to you.