I had the same problem; I'm extremely frustrated with base Rimworld because so much of the game requires tedious micromanagement. I've finally realized that playing without 15+ mods is a terrible idea; not mods that change the game, but mods that add logic the base game should have had by default.
Kostriktor, take a look at this one, I think it might help you as it should force animals to move to the caravan packing spot on their own: https://steamcommunity.com/sharedfiles/filedetails/?id=2068456092
Kostriktor, take a look at this one, I think it might help you as it should force animals to move to the caravan packing spot on their own: https://steamcommunity.com/sharedfiles/filedetails/?id=2068456092