Not sure if this will work for you but we put up a secondary fence alongside the chain link fence we share with our one neighbor - now there is a 2-3 foot area between the fences. So our neighbor's dog has 'his' fence and our babies have 'their' fence. Occasionally they will let out a bark or two when they first see each other in the mornings but mostly they just watch each other through the double fences
BTW, the secondary fence is not a big fancy fence. We made it out of a roll of 4' high garden fencing and stakes - pretty easy to put up.