I love dogs, but your poor boy being frightened and his own nan and aunt not seeming to give a shit. 😔 That's awful.
You can't change their behaviour but you can change yours. Stop taking your kids to where your sister and dog are for a start. It's not fair on your poor son (or the dog) if he's scared and understandable screaming and crying when being jumped on. If this means that your mum doesn't get everyone together for family occasions, tough. Your priority is your child.
Hopefully, when they realise they're missing out on seeing you and your kids, they'll see they need to compromise. Leaving the dog at home if possible, or keeping the dog separate from your son are perfectly reasonable requests.
Honestly, if they're not willing to change, are these people really who you want around your children?
In terms of his phobia, if he wants to try not to be scared, there are things that can help which you can google. He may just need to meet some lovely, calm dogs that are trained and don't jump up! Why has your sister not trained her dog anyway? 🙄 Your son may never be a dog person and that's ok, but it's probably worth trying to get him to the stage that he's not frightened, just because he's likely to encounter dogs in life.
The most important thing is to show him is that you'll help him by removing him from the situation he's scared of.