Is it permissible to accept compensation from the family of a young child who caused damage to a car window, knowing that the repair costs are exorbitant?

The boy is liable for what he damages with his own money. If he does not have money, one waits until he acquires it. His guardian or family are not obligated to pay compensation unless they volunteer to do so. It is permissible to accept compensation from the boy's family if he damages something.