If you appear as a driver on the company's insurance policy and you're specifically assigned to that vehicle, you may not need another policy. If the policy excludes personal use of a business-owned vehicle, then you'll need to consider obtaining a separate car and policy for personal use. The answer is to add an endorsement to the personal auto policy, known as extended coverage for designated non-owners, to the personal auto policy. Each member of the family must be included in the endorsement if there is any chance that they may be driving the company vehicle.
Most commercial insurance policies will cover you when you drive your car for a business delivery. However, there is one exception. If the delivery of goods or people involves paying a driving fee, your personal vehicle insurance company will invalidate commercial auto coverage.