Welcome to the forum Spayne!
I am not aware of any vines or even plants for that matter that repel mules specifically.
There a few plants that are know to repel deer, and you might give them a try. None of them are vines either, though.
- Hens & chicks
- Lamb's ears
- Red Osier Dogwood (cornus sericea 'allemans')- This is a tall shrub
- English lavender (lavendula augustifolia)
I will keep my eyes out for you. People who live here are constantly coming up with ideas of how to keep the deer away, they are very common. One way that several use is to use a motion detector on a water sprinkler. When motion is detected, the animals get sprayed!
Best of luck, I know it can be a problem!
Feel free to drop in again anytime with questions or just to chat!