I have Both DLC pack downloaded and they are visible when i check the storage on my hard drive but i can not play them unless i am online. I have not update the xbox i play on in a while since i dont have internet access near it so i swap hard drives on the one connected to the internet. Download the content then Swap the Hard drive back to my offline system. Do i need to update my Xbox, or is there something else i need to be doing??

DLC content is tied to the XBox it was downloaded to, not the HDD

if you want content on 1 particular XBox you will need to connect that one to online and license transfer to that XBox. Otherwise you will need to be connected to live to use the content.