I heard the idea from someone else, but shepherd's cane/crook seems like it would be a better concept than a carrot on a stick.
Elaborating on the idea tho, I think a cane could let you move them like a wheelbarrow, but whether that animal listens to where you tell it should be based off of your CHA and/or STR, maybe the higher of the two?
Maybe have a x*y cap that once you pass it, they always listen. So as to take the grindyness out for dedicate players, also to give new players more incentive to get better
Idk im just throwing ideas out there, but I would like to be able to wrangle animals in smaller pens a bit easier.