Can parents be sued for liability for a child on their auto insurance policy while a daughter drives her own car and is not living with parent and a title of her car is on her parent's name?

Yes, The owner of a vehicle is just as liable for an accident as the driver. Both the driver and the Vehicle owner are both jointly and severally liable for the cost of an At Fault accident.

Since you say the title is in the parents name, Then the Parents are in fact the legal owner of the vehicle as far as the state is concerned.

The at fault driver is liable because they caused the accident, The Registered Owner is liable because the owner has a responsibility to ensure that all permissive use drivers have the appropriate insurance coverage before allowing them to operate the vehicle.

Yes, If your daughter is still a minor, the legal guardian (usually the parents) can be sued under parental liability statutes even if the vehicle is not owned by the parents.