Yes, everyone in your household should normally be listed on your car insurance policy.
You need to disclose all household members when applying for car insurance. Typically, an auto insurance company will then use the information you have given to include drivers on the policy, exclude drivers from the policy, or not rate certain people on the policy.
All household members should be known to the car insurance company, but do not necessarily have to be listed as covered drivers depending upon the situation. For instance, if you have a son that is 16 but not yet licensed and so he doesn't drive, they may require that you list him on the policy but will not rate him until he is licensed.
If your children live with you and are licensed drivers, they would need to be listed on your policy so that they were properly covered. If your son and daughter have already moved out of your residence, then usually you do not have to list them on your policy. They instead would need to get their own car insurance policies for the vehicles each of them drives.
If your children do not live with you, but still occasionally drive your vehicles, you will need to inform your car insurance company. Your insurer then may or may not require you to have them on your car insurance policy as occasional drivers. It depends upon the insurer's internal guidelines.
In general, anyone that drives in your household and sometimes also those outside of your household that on a regular basis use your vehicles should be listed on your policy.
Without knowing about all household members and frequent drivers of your cars an insurance company cannot properly calculate the risk and then the premium to be charged for the policy. If you fail to tell your auto insurance company about any children in your household and they are in an accident, claims could be denied due to misrepresentation.
Talk to your car insurance agent about your specific situation and who your company requires you to list on your policy. If you find that your current insurance company cannot fulfill your car insurance needs, contact CarInsurance.com.
We have agents that can explain insurance terms and policy requirements as well as help you get low cost car insurance for you and your whole family.