Liability laws can vary from state to state. To find out for certain if you could be held responsible in any way in California, if your daughter was in an accident that exceeded her car insurance limits, due to being the policyholder first check with your insurance agent since he or she knows the specific terms of your policy and if you still have questions regarding possible liability then check with legal counsel.
It might make a difference if your daughter is still listed as a dependant on your taxes since this normally shows they are under your parental rules. If your daughter was under 18 and thus still a minor, your liability would be more then it is now that she is 18 and considered an adult.
Parental liability according to California law provides that parents, or the parent or guardian having custody of a minor, are responsible for damages resulting from a minor's negligence in a vehicle accident. This will occur when the minor is driving a vehicle, any vehicle, with the express or implied permission of the parent or guardian or if the parent or guardian has signed the minor's CA driver's license application (required as a condition of issuance of the license).
Liability in this type of situation is limited, however, to the financial responsibility limits imposed by law (Vehicle Code 17709): $15,000 for injuries to one person in a single accident, $30,000 for injuries to all persons in a single accident, and $5,000 for property damage in a single accident. If an accident involves a minor's "willful misconduct," the Civil Code imposes an additional liability of $10,000 on the parent or guardian having custody of the minor, whether or not the parent has permitted the child to drive or has signed the license application.
We have read that CA laws can impose unlimited liability on parents if children (of any age) are driving a vehicle while acting as the parents' agent or on an errand at the parents' direction. Unlimited liability is also possible if the parent negligently entrusts the car to a child known to be an unsafe or dangerous driver.
Another place to get information on what your liability could be for 18 year old daughter is the California Department of Insurance. Their consumer division may be able to give you advise on your current situation and CA liability laws,