We are cat lovers, but are surrounded by dog lovers, whom we are friends with. We have never had a problem with a neighbors dog. All of them have been very careful when walking their dogs and having a bag handy for the occasional poop.
Very sorry to hear the OP is having a problem, and I hope that a common ground can be found so this does not escalate.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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