The rules were recently clarified, and yes, you can have a rifle in a caravan, but if I recall correctly the security needs to be inspected by a member of the police.
From the police website...
Secure storage of firearms and ammunition in mobile homes (regulation 19A)
Firearms and ammunition may only be stored in a mobile home, campervan, or caravan unit, if the vehicle or unit is being used as a temporary or permanent home; and the licence holder has appropriate storage that has been inspected and approved by Police.
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