I am sorry to hear about Jessie.
Dogs growl at other people for a variety of reasons. One is because they are afraid of the person, so I would ask questions to be sure that nothing ever happened to make him fear these two people. It does not necessarily mean that they did anything really bad to him; dogs can react to subtle messages, like eye
contact and body language.
Another reason for him to growl is if he thinks he "owns" you, and that he is protecting you. Do these episodes happen only when he is near you, like on a couch or bed? Or does it happen just anywhere at all when all four of you are in the same room?
Yet another reason could be that he sees your husband and son as threats to his social position in the family. Dogs are pack animals, and usually have a strict social hierarchy, and Jessie might see himself as higher in the pack than he should.
Is Jessie neutered? If not, that might help a lot.
Ignoring it is not the right thing to do. If you ignore it, you are telling Jessie it is OK to act like this, and the problem will probably get worse.
If you want to train him to stop doing this, you probably need to work with a veterinarian with problem behavior
experience, or with a dog trainer. If the problem is fear, you need to train him not to fear your husband and son. If the problem is him thinking you are his property, or that he has more social standing than your family members, then you have to train him to think otherwise.
If you are the one that feeds him, that would reinforce his belief that he "owns" or is the boss of you. I would have your son or husband start to feed him, and you stop. I would never let him up on the couch or any elevated place next to you; sitting on an elevated place is a position of power in dog body language and if a dog growls at a person or another dog when up on furniture, then they should not be allowed up on furniture at all. Obedience training
is the core of any dog training
. Spending a few minutes every day reinforcing Sit, Stay, Off, Down, etc. is the cornerstone of training him to behave as you want him to. If he has never been to obedience class, if he does not immediately obey commands like these, he needs to get some obedience training. Then you could ask the trainer to help you on this problem.
Behavior problems can be as complex as a physical illness. You need to get a specific diagnosis of his problem ( dominance aggression, fear, misplaced aggression, etc) before knowing the the best way to treat it. I do know that if you do not do something, he will get worse, and some one could get bitten. He needs to learn how to be part of the family, on your terms, not on his.
Good luck with Jessie, Rebecca