@Ladygray
I totally understand what you're going through and do not think you're a busy body for wondering about your new neighbors. You have my sympathies for having to put up w/ a dog that has not been trained by the owner and for people who let their yards go. And yes, dogs poop in the yard ... but it should be picked up so the neighbors don't have to smell it. I mean, c'mon.
I have lived in the same house for years and we have only had a few ownership changes. We did have one neighbor who left their dog outside (fenced yard) during the week while they were at work. The dog was older and he would charge the fence every dang day we were outside, multiple times a day. It was scary to me and it made our own dogs so crazy we had to keep our dogs away from that side of the yard. Let me just say I was glad when those people moved.
What I go through now is selfish dog owners who do not think rules apply to them. I run in a park that say Dogs must be on leash and controlled at all times. More than half the people do not believe that rule applies to them. I have been charged by countless dogs, so I carry a small horn and pepper spray. Never once has an owner said they were sorry their dog charged me ... they say, oh he/she is just so friendly. When I ask why the dog is not on a leash they get snotty w/ me and tell me no one else minds. I've never used the pepper spray, but I have used the horn many times.
My only advice is to contact your landlord. Since you have been such a good renter, you might just reach out and let them know there are issues and you would like their help or advice. If it's a HOA issue, they would be the ones to contact the Association. Also let landlord know about the overhanging branches, etc.
Good luck and I'm so sorry you can't go outside w/o dogs barking and being a pest. IMO it's the dog owner who is to blame, not the poor dog.
"What we practice daily is what we build a life on. Practice peace, love & kindness."