Harment by Neighbors, Landlord's Obligations?

My grandma is having a very difficult time at the townhouse where she lives, and this may lead to a long description of the problem, but I'm trying to help her decide just what sorts of legal action need to take place. Some new neighbors moved in about six months or so ago, during the time the townhouses were going through a landlor transition (some new people bought the places). My grandma has dogs, and there is a field out back that she takes them into to poop. It's owned by a grocery store, and the owner has told my grandma to her face that she CAN take her dogs to poop there. Apparently, the neighbors don't like that she does that, so one day, as my grandma is getting into her car to go to work, she discovers dog poop packed under her car door handle. That was the start of everything. Since then, the neighbor's kids throw at the side of her house (she lives at the end), they've knocked over plants, birdfeeders, and even her concrete birdbath. The mother even went so far as to physically ault my brother's girlfriend isn't even 5 feet tall by grabbing her face. I know for a fact that my grandma can press charges against this ***** (pardon my French, but this is my GRANDMA this woman is haring!) and I've been trying to talk her into doing so, so she's having me find out everything I can so she build a solid case. Now, the question is, what is the obligation of the landlord in all this? My grandma has gone to them several times seeking some sort of help and they literally told her, "So?" All they care about is the money and my grandma is thinking about stopping paying the rent because she feels so threatened. She says she can't sleep during the day (she works overnights, so needs her sleep during the day), they swear at her and our family that lives with her. I'm sick of hearing about it, because it should never have happened in the first place--my grandma is perfectly harmless and keeps to herself. She's lived there for 11 years, has never paid rent late,and has never had problems with any neighbors before.