Neighbors Won't Keep Their Chickens Off My Property[virginia]

Had new neighbors buy a house next to me in the past 6 months and decide they want to be backyard farmers. However, they didn't finish the fence between our properties and let their chickens run loose and for some reason they prefer staying on my property, crapping all over my porch and even my vehicles. I also own chickens, ducks and cattle. The cattle are enclosed in their pasture, ducks and chickens have their own enclosures as well....nothing is free range. I keep my dogs in outside kennels during the day and I've noticed when I'm feeding them during the day the chickens run up and try stealing food out of their kennels. I went to the neighbors and told them they need to keep their animals on their property, that the chickens are becoming a nuisance and just got "oh we'll take care of it" in response. This morning my dogs killed one of their chickens when it decided to stick its head in the cage after some food and now the neighbors are threatening to "press charges". Should I be worried?