We have a Family policy. Are my children covered if they travel to another city without me?

Dependants on Family or Single policies MUST be with with at least one of the adults listed on the certificate of insurance for 100% of the person travelling’s itinerary

If dependants travel to another city or accommodation without at least a parent or grandparent listed on the certificate of insurance, there will be no cover for any claims that arise.  For cover for your dependant in this situation, you should purchase a separate Single policy for them.
Cover is subject to the policy terms, conditions, limits and exclusions in the Product Disclosure Statement (PDS).