Can a parent be held criminally responsible for allowing a child to go with an adult that was under the influence and caused an auto accident?

Most states have what is called a "risk of injury" statute.  under this statute, a person may be criminally liable for placing a child in a sitiuation where it is exposed to bodily injury or harm.  the statute is very broad as to what constiutes harm and the statute does not require that the state prove that the person intended to expose the child to harm.  rather, the staute has negligence stardard - i.e. knew or should have known standard.  in this case, if the mother know or should have known that the driver was under the influence and was not capable of driving safely or should not be behind the wheel, then the mother may be held liable for this particular crime as the kid was placed in harms way.  if something happened to the kid, then the mother can be sued for negligence and collect monetary damages from her as well as the driver.