out some of your dogs shit in a ziploc bag..and put it under a cushion on their porch..or behind the tire of their car. (or stick it on their mailbox..right on top of their mail.)
You got a 'notice'? Someone sued you because pigeons landed on their house? When the police came out, what they say they were responding to?
It sounds like there's some serious misunderstanding here or else you live in a development with some rather strange HOA rules. Either way, the specific things you mentioned don't sound terrible. I don't see why your dog has to poop on other people's property even if you do pick it up, but I can't imagine calling the police over it or why they'd even bother to show up. The pigeon thing is just stupid. There are real community rules in some areas about when you can put out trash and when you have to pick up the cans, but again, I can't see the police coming out for that. There's something else you're not telling. And your neighbors really are insane.
That was silly to tell them to put dooky on their mail; tampering with mail is a federal crime.
You should never feel like you have the right to tresspass on other people's property.
I bought my house two years ago, the first fall I came home from work and my neighbor was burning a big pile of leaves in my driveway; I couldn't even get my car in the garage. When I asked her what she was doing, she said she had lived in her house for decades and always burned her leaves there. I think she may be a brick shy of a load in my opinion. I just took pictures and my insurance agent is keeping a file on her. They throw limbs in my yard; they are from their trees I don't have any!!!