I loathe the nasty things, but we have so many around here that we would do nothing but kill possums from morning to night.
I think they smell the dogs and kind of sheer away from our property. We also have catches and bungee cords on the garbage cans so they can't get in, and we NEVER leave anything edible outdoors (I know you can't do that on account of the horses. I know Gracies is a sloppy eater and there's grain all over the ground around her feed pail). Good sanitation also keeps the raccoons away, which is a good thing because a big boar raccoon can kill a dog.
I leave food out for the barn cats... But lots could be made more secure. If we moved the food up high where only the cats can get it, and worked at sealing off under the house where I think the possums have been living, let the dogs out more at night since we have the last of the kittens (the mommas are smart) and take away all the possums we catch, THEN we can get rid of at least this family and hopefully not attract a new one.