If there have been on-going issues a mediation session should be arranged between interested parties. The exact nature of the complaints against the dog have not been mentioned but perhaps the owner is concerned that someone is teasing the dog. I believe the concerns of a common area being filmed are vexatiously exaggerated. We can’t make our problem neighbours get psychological counselling. We just have to move from a toxic environment.
Filming of common areas, such as the footpath or street, can assist with crimes.
I have a dog but keep her inside when I go out. Dogs are less likely to bark when they are kept inside.
I speak as someone who has had their house burned by a paranoid schizophrenic neighbour and also shared a wall with a drug, alcohol, domestic violence abuse household.