What about proceeding on negligent homicide?
The requirement for "negligent homicide" is usually that
(a) that the defendant's conduct resulted in the death of the alleged victim; and
(b) the "person ought to be aware of a substantial and unjustifiable risk that the alleged victim will be killed.", Further, "The risk must be of such a nature and degree that the failure to perceive it constitutes a gross deviation from the standard of care that an ordinary person would exercise under all the circumstances as viewed from the accused person’s standpoint"
[taken from http://www.tncrimlaw.com/TPI_Crim/07_07.htm]
This is Tennessee law. However, laws in other common law jurisdiction are similar on this offence.
I think that any parent would be aware of the volatile nature of 13 year old girls, and as it could be shown that she had such knowledge, it may be possible to proceed.
That said, I think there is a case that legislation should be enacted to allow criminal prosecution to proceed under a "felony murder" rule; that is, once negligently/recklessly causing mental injury to a minor is shown (which would be the felony), the intent transfers to the subsequent suicide (since we have proximate cause), and prosecution proceeds on first-degree murder.
This does, of course, mean that you need to define a "negligently/recklessly causing mental injury to a minor" offence.
Biting the hand that feeds IT
