Even though a piece of property may seem like junk to one person, it does not vest a right in another person to damage or destroy the property.  Until your children reach adulthood, you are responsible for any damage they cause to another person's property.  Causing damage to someone else's property is generally filed as "criminal mischief."  In addition to civil liability, your children could face juvenile charges.  If the value of the property damaged it under $1500, they would face a misd probation.  If the damage is over $1500 they would face felony juvenile probation.  Under civil or criminal settings, you would be ordered to pay restitution on behalf of  your child.  The only limit is that the amount ordered has to be reflect actual damages.  The owner doesn't get to ask for "emotional" damages in the criminal setting.  How a victim is made whole depends on the parties.  Many victims want restitution, but others can and do accept repairs as sufficient restitution.  If you think the restitution request is unreasonable, you have the option of contesting the restitution amount through the court systems.