More facts are needed. Was anyone injured?
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Generally, as you state the question, the vehicle owner who permitted the child to operate without parental consent would seem to bear primary liability. The specific law that applies will differ depending upon what type of vehicle it was, as farm implements, recreational vehicles, and vehicles licensed for operation on the roads are addressed by different statutes. That doesn't stop a plaintiff looking for coverage from suing you anyway, so report the incident to your insurance company.
This answer is provided for general information only. No legal advice can be given without a consult as to the specifics of the case.
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