Rather than this becoming a slanging match over which family member gets chained up outside, this could actually be a good opportunity for you to have a positive & lasting effect on your Nephew's life.
As a child, I was petrified of dogs into my early teens.
We didn't have any pets, so the only animals I came into contact with were at friends & relatives.
Cats - Fine.
Dogs - I would (and did) wet myself rather than cross the hallway past the sleeping dog to get to the toilet!
For me, the breed, age, temperament, etc. of the dog made no difference. Even the old, frail, sleeping most docile dog on the planet - I'd be terrified to go near it.
To me, it was just a wild beast that was taking an unhealthy interest in my every move. And it wouldn't go away even if I asked it to!
My biggest fear was being bitten by them.... And because dogs naturally sniff everything - that means their nose and and teeth are getting a lot closer to me than I was happy with - Basically I was terrified of getting bitten or jumped up at ripped apart with its sharp claws!
(as an adult, I realise how silly that sounds... but 12 year old me was terrified of those sharp looking teeth & claws and that snarly, growly noise dogs make when they're just playing and talking "dog"!)
It turns out that one of the "mistakes" I was unwittingly making was to approach a dog and try and stroke its head.... Naturally that made the dog tilt its head upwards to follow and sniff my hand... and that meant those scary teeth getting near my hand again - Fido was clearly trying to bite me and I wanted out of there!!
(a bit like the story of the gingerbread man - when the boy is sitting on the fox's nose, then the fox flicks his nose up and eats the gingerbread man!)
But a lifelong family friend a dog-owner observed what I was doing, how I was interacting with their dogs and what about their dogs that I seemed to be afraid of, or what I was doing that the dog didn't like.
They demonstrated on me - stood up tall above me, reached down to stroke my head - naturally I looked upwards and they pointed out that that's exactly what the dog is doing! - And it clicked!! :D
Thus, they showed me how to tickle the dog under the chin rather than reaching over its head, so the dog was happier and didn't react in the way that scared me.
That family friend, along with another dog-owning family friend (and, in hindsight, their wonderful dogs!!) both completely transformed my attitude to dogs.
Over the years, they observed how & why I was terrified of their pooches. And helped me to understand things from the dog's perspective.
Sometimes they would put the dog on the lead or hold its collar and encourage me to approach and interact with the dog.
Whilst at the same time explaining to me what the dog was thinking.
"He's excited 'cos there's somebody at the door - just like you come to the door and greet us when we visit you"
"He's not barking 'cos he wants to eat you - he's barking 'cos he wants you to play with him. Here, why don't you get that squeaky toy and throw it down the hall for him. See - he likes that!"
"Put some of these biscuits in his bowl for him - see - you're his best friend now!!"
Help them hold the lead when out for walks, etc.
As an adult, I'm fine in the same room and even stroking the most boisterous of dogs!
I owe that entirely to those two family friends & their various wonderful dogs.
I'm not saying that its your responsibility to "fix him"... but if he doesn't have a dog at home - your dogs in your home and around your family would be a good "familiar environment" to help him build his confidence over time. Rather than just isolating the warring factions every visit.
Those friends changed my life - you could do the same for your Nephew :)