On the other hand it is easy to teach a dog that they have to stay away from you & only you (mine while they are staying at my folks know what they can get away with with them but when I am home visiting they are perfect angels) I agree, a few shots of citronella spray, though some dogs need something "tougher", I always used something called "Wrap Last" which is essentually pepper spray, its actually something you spray on stall bandages to keep the horses from messing with them.
One shot of that in the face & most dogs will not do it more then twice, its better then lets say, their dog & your dogs having a free for all when one or more of them get sick of being harassed with they are trying to use the restroom. Not to mention it can regress your training (having dogs that will start to not use the restroom for fear of being bombarded by some obnoxious dog).
That is if they say no to the tieing him up thing while you are outside but I would not lie about the reason, I would be straight foward with them, I would say in a diplomatic way that your dogs aare unable to use the restroom even because their dog is bothering them & then ask if you guys can compromise on just tying the dog up when you are outside letting your dogd do their business, then taking your dogs back inside, then letting their dog off.
you could also make a date where all the dogs can be outside playing together for further compromise or something like that (not during your dogs "bathroom time") maybe after your dogs have used the restroom or something like that.
also maybe you could offer to work with the dog to make him more neighborhood friendly to benifit everyone.