I’m using an iPad v12.2 most current. I’ve unlocked the first processing queue, but do not have..

So the game devs really jacked up the DD update this time and its so much more different than last. First if you have more than 1 AC then you should place down all your honor structures. Secondly, even though you don't use all your processing plants you've placed down, they do add up together so they process faster and hold more per queue. Thirdly, To unlock more queue's for processing other resources, you need to research them in specialty under "construction specialty" then there's 4 tree options 'left, right, up, down', The tree on the left will make you able to unlock more queue's.

Quite possibly to unlock a second queue you'll need to place down the second processing plant if you haven't yet. You kind of didn't explain much so maybe what I said might help.