We had trouble with our neighbors when we first moved in, and the nearest house is almost three acres away. I think you are on the right track, Farmettehopeful, to understand that your neighbor is overly hostile because of jealousy. It is sad, really, that she is so unhappy with her situation that she is focusing her energy negatively on your guys. You mentioned her kids - I wonder if they are also suffering from such a negative environment.
She may never come around, unless she is able to deal with her own demons. But you are the better person, hands down, for trying to have that conversation with her and trying to get some understanding. No need to waste your energy stressing about what they think of you. Just let her tirades roll off your back and think to yourself, Wow that's sad. Be honest and cordial. And good luck.
Our neighbors were angry that our property was willed to us, as they own a big apple orchard to the side of us and were hoping to add this land to theirs. They complained about everything for the first year - I'm a night shift nurse and they gossiped about me driving in and out at odd hours, they complained about our dogs barking (from several acres away, and ours are definitely not the only dogs you can hear barking!), about our lawn, which is more of a meadow really, not being mowed, among other things. So I told them about my job, started putting the dogs in at night, and stuff like that. Man, I used to dread coming home in the morning and seeing that guy driving his tractor up the street to meet me, after working all night, because I knew he was coming up just to complain about something before I had even finished getting out of my car! But you see, they were upset they didn't get the land, and were suspicious that we were irresponsible young 'uns who weren't going to use what we got.
Finally after more than a year, the complaints stopped, and we now wave hello to each other. I'm going to invite them over to see my chickens before the roosters start crowing, that's for sure!! But my suspicion is, they will be showing up a lot more often - for eggs and a handshake.