Hi A.,
I think it's perfectly normal to feel the way that you do. However, I think you need to first try to understand the dog. Many smaller dogs are actually afraid of children, which is why they will bite. If the dog is not around children much, this would explain its reaction. You had said that your son was running toward the dog. It's possible that the dog, being chained, might have felt threatened and trapped.
I would not ask your parents to put him down or even to get rid of him. Instead, I would simply ask that he be put away where he cannot reach your son when you are visiting. Also, you need to be proactive as well and make sure your son knows that the dog is off limits. In other words, don't let him go into a room where the dog might be. Or don't let him go within proximity of where the dog is chained.
Deaths that have occured as a result of dogs attacking, generally are from breeds such as the pit-bull and Rotweiller. These are very powerful dogs. Jack russels are not known for killing children (at least not by themselves.)
I have three dogs and a six year old daughter. One of my dogs is a great-dane/lab mix. The other one is some kind of lab mix, and the last one is a chihuahua mix. My daughter has been injured a few times because of rough play. Twice, when my daughter was younger, my older lab mix showed some aggression toward her. Both times she literally pinned her down and barked into her face... looking as if she were biting her (but thankfully she only yells and has never bitten anyone). This is how my dog shows her dominance. Both times this occurred when my daughter was younger (about one or two years old) and both times my daughter was going into my dogs personal space/territory. Additionally, my dog was simply not used to kids and was used to being the center of my attention. She didn't hurt her though, but I remember being very angry and frightened and grabbing her by the neck and tossing her 85 lbs body out the door. I still have the dog, and today they are both best friends and the dog totally obeys and even protects my daughter.
Finally, I would understand giving the dog away if it was yours. I had always said that the first time my dog bites my child, she's out of here. However, the dog is not yours and you do not live at your parent's house. Don't punish your parents by making them get rid of the dog or by refusing to visit. Simply maintain control of your environment and your son and understand the dog's point of view. He's obviously not used to children so don't impose any child on him.
Oh, one last thing. I've also taught my daughter to never go up to a dog unless she first asks permission from the owner and then to proceed carefully. Of course, your son is still young, but he's almost at the point where he should understand this. I think my daughter was about two or three when she figured it out.
I hope your son is feeling better and I hope this incident does not make him afraid of dogs. Dogs sense this and can react when they sense someone is afraid. Whenever my child has a friend come over and play, I always ask, "Are you afraid of big dogs?" If the answer is uncertainty or yes, I will always put my two big dogs out of reach.
I hope this helps.