I ended up fixing this accidentally and I think I figured out the cause.
It seems that if a wolf has too long of a name, they do not show up in the trade/attach selection box in a message. Half of my den wasn't available but there didn't seem to be any rhyme or reason. Changing the name of one to be shorter (some are close to the character limit) suddenly made it show up. I tried on both mobile and desktop with the same results.