I agree with Lee, Marv, and Gogar. This could get ugly fast and that would just not be very fun since it will be a long time, considering they just moved in. Direct and nice guy is good. But I would like to say that ultimately, it is their property and even though it is the country and it seems everybody is really nice in the neighborhood except this b*%*#!, you can't really get mad at her for wanting her property to be, well, her property. She will just be the house that gets egged at Halloween.
Maybe try to build a smaller enclosed/fenced in area on your property for the dogs? So then you don't have to build an entire fence for your property.
Sucks to have no bueno neighbors.