my child was in a car accident while under our insurance. Can we be sued by the other parties?

Assuming your child was legally operating your vehicle with your permission, it is unlikely that you would be sued by anyone that he may have injured.  Parents can be responsible for the negligent acts of their children, but in a situation such as this, you had no control over his actions behind the wheel, and thus could not be considered negligent.  In Indiana, insurance follows the vehicle, not the driver, thus your insurance would cover your child in the event that he/she would be sued.  This would also mean that your insurance company would provide a defense for him/her and pay out any settlement or verdict up to your policy limits, if appropriate. As an Indianapolis attorney who has represented both insurance policy holders such as yourself, and injured motorists, I can tell you that this is not an uncommon occurrence.  If you have any questions about your specific case, please do not hesitate to contact me.  Initial consultations are always free of charge.