It is illegal in the US for an employer to do or say ANYTHING about an employee other than to confirm the dates that he or she worked for the company. Even giving the reason why or how a person left the company is illegal.
If your employer is giving out more information than that I can help you find the laws. You would then send a letter to your former employer demanding that they stop this. You could also file a lawsuit AND WIN easily.
I learned this as a manager and again in several business law classes.
You can be fired at any time if an employer learns you lied in an interview or on an application, so the truth is vital. Details, such as difficult child being a difficult child or in Department of Juvenile Justice or anything else, are not needed. Just give dates, and say the LOA was due to a now resolved family matter. It would be a good strategy to IMPLY that it could not happen again - as if it were a family member who has passed away. Don't SAY this, but state that it has been "permanently resolved" or something similar.
JUST DO NOT EVER EVER EVER TELL AN OUTRIGHT LIE.