So, dh and I bought a house in May.  Everything was good, until the neighbor wife came over and gave me a rundown of who 'sucked' and who didn't, who has dirty secrets and who doesn't, how the previous owners of our house were abusive to their children and his wife, and how they ran him and his wife out of the neighborhood (like it was something to be proud of), and a lot of other neighborhood drama.  All of which I could care less about, being as I'm not 16, and dh and I keep to ourselves.
We were friendly for a while, and then she had surgery.  I told her I would try to help her if I could, but that I couldn't do much, because I was in a walking boot, and I have a 5 year old who wasn't in school yet.  Dh had to go to a class for work  in OH (and the class is 5 minutes from his parent's houses) so, rather then leaving us at home, we all drove there.  I shot her a text telling her we'd be out of town for 2 weeks, and to see if her husband could make sure nothing looked out of place outside.  She replied with "I thought you were supposed to take care of me"  yikes.  I had my old neighbor come by to pick up mail and feed the cat every other day, becase, as my neighbor said, she couldn't do much, because she just had back surgery.  My other neighbor called and said that we hadn't had any mail in 4 days, and I found out my crazy neighbor took it, thinking she would be helpful- so I told her I had someone coming by already taking care of that- and she freaked the eff out, and didn't put my mail back till the next week.
Moving on to a couple weeks later, I found what appeared to be either a mistreated dog, or a dog with allergies, because it was missing fur in patches.  I cleaned it up, and she offered to help, so I let her.  Then, since I had 2 dogs at the time, dh said we would keep it in the bathroom overnight, and take it to the pound/vet in the morning to see if we could help it/find it's people.  She wanted to keep it at her house, and I said fine, that way it wouldn't be stuck in a bathroom all night, and they had no pets, so if it did have any diseases, our animals wouldn't be at risk. 
Well, she took it to the vet, and microchipped it in her name, and didn't bother looking for it's people.  They said they drove around the neighborhoods looking for flyers (which I later found out from the actual owner, they drove around taking them down)  Right before school started, I saw a flyer looking for said dog and it had a number on it, and I texted my neighbor to see if she saw the flyer, and she basically said finders keepers losers weepers.  DH went over there, and asked if they would reconsider calling and telling them they found her dog, and she said that they spent too much money at the vet getting her fixed up, and they weren't going to giver her back. 
My mom can be a bit abrasive sometimes, so I called the number on the flyer, and was going to undo any damage she had done, and found out that my mom was the 5th person to call about the whereabouts of her dog, and that she had tried to go get her, but she slammed the door in her face and told her she didn't have a dog. The owner got mad and had some people um,
vandalize their cars.  They threw a brick through her back windshield and threw paint on his car, and according to the crazy neighbor, threatened them until they gave her back.  While the police were outside taking their statements, the husband was giving my husband all sorts of dirty looks,and my dh told me he was going to wait to go to work, because he didn't
trust them, so he waited on our driveway for me to get home (we live right across the street from the school).  They decided to clean up the mess an hour and a half after the cops left, when all the parents were walking their kids to school, and proceeded to yell at dh at the top of their lungs calling him every name in the book (in front of children- and in his
uniform- dh is military) and told passersby that we did this to their cars, and that we're awful people, etc.  I could hear her yelling all the way at the school, so I ran home and wanted to show her that that's not how you do things, but dh told me not to, so we went inside, and he went to work a short while later.
Ever since then, they have tried to make our lives a living hell.  They mock us because of our vegan life style, they stare us down everytime we come and go from our house, they have their kids say rude things to us, and stare us down, and any time they have people over, they get them to do it too.  It got to the point where I didn't feel safe, so we got another
dog, and we were going to put him in training to be a guard dog (which I now see was lame).  They backed off in the winter (i know, it's still winter, but in TX it's not winter for long) and now that it's getting warmer, they're back to the same crap.  I've called the police about it, and they said technically they arent doing anything wrong, because they're acting
like little kids in the back seat of the car "im not touching you..." (when I called them when they were yelling at dh, they came, but they didn't file a report, because he thought the neighbors actions were justified, being as he was the one who took their statement...wth??  So, now, we have to deal with their crap, and as much as I try not to stress about it,
I can't help it, because I'm pregnant, and my hormomes are all sorts of messed up.  We are trying to be the bigger person, by not saying/doing anything, but they're making it really hard. What really sucks, is they rent and we own.  I called the previous owner of the house, and he said they pulled the same stuff with them, and made up all sorts of rumors about
them, and that they won't stop until we/they move.  HOA won't/can't do anything about it either.  I'm fed up, and normally, I would try to talk it out, but there is absolutely no reasoning with them.  Moving is not an option.
I'm fed up, and there's not a lot we can do. 
So, my question is... what would you do in this situation?