It sounds like you have an extremely irresponsible neighbor! I would be really annoyed to have their animals running all around my neighborhood, bothering my own animals! I say start eating ALL their chickens that roam into your yard. If they come over, they're DINNER! Get 'em before your own dog can! LOL
I'd be calling the dog catcher on their dogs too. I hate when people can't take care of their animals like they're supposed to! Grrr!
I don't even like my neighbors cats in my yard, upsetting my own cats, looking out at them from inside our house. Keep them at your own home!