Your daughter is still a member of your household, so normally car insurance companies will allow her to remain on your car insurance policy. In fact, if her spouse lives in your home, then he too should be added to the policy as a driver.
Being a driver on your car insurance will allow your daughter to drive your vehicles. If your daughter and her husband have a vehicle of their own, that is titled and registered to one or both of them, then typically insurance companies will want your daughter and her spouse to get their own policy, under their own names, for the vehicle.
Most car insurance companies want you to have insurable interest in any vehicle you place on your policy. Basically, this means that you own the car. If you aren't the car owner, then it is hard to get insurance placed on a car in your name, however, some auto insurance providers (like Esurance) do allow it.
If your daughter and her husband own a car of their own, you wouldn't have insurable interest in it to place it on your policy and instead they will need to get their own auto insurance policy.
Whether they are on your policy or get a policy of their own, if both your daughter and her spouse are teenagers, then their car insurance rates will be high due to their age and lack of driving experience. (See "A parent's guide to insuring a teen driver").
To help lower rates, ask about discounts. If they are still in school, then they may qualify for the good student discount. If there are multiple cars on the policy, you should get a multi-car discount.
With teenagers on your policy, it is a good time to do car insurance comparisons and make sure you are getting the cheapest rates. You can use CarInsurance.com to automatically find the best rates available.
We offer multiple company insurance rates for personal auto insurance and the ability to purchase from one place. Start your free auto insurance quote here.