要他們家的 home owner insurance

http://www.nolo.com/legal-encyclopedia/does-my-homeowners-insurance-cover-accidents-that-occur-off-my-property.html

The good thing is your homeowner’s policy usually covers you and your family’s negligent behavior no matter where it happens. For example, if your son accidentally hits a baseball through your neighbor’s window and you have liability insurance, it is probably covered. If your toddler son darts in front of an elderly woman walking in the mall and causes her to fall, your policy should take care of her injuries too.

HOI一般不覆蓋受保人的故意傷害（比如故意打人甚至犯罪）。 所以，如果你走保險一條路，你必須闡述這個事件是意外而不是故意。

如果對方沒有HOI，你的任務是研究你們州關於父母對於小孩的賠償法律。Google, parental responsibility law  50 states。有的州隻是規定父母為小孩開車意外事故負責，而不是對小孩所有意外負責。