I'm going to preface this answer to state that I think the physical issues you describe in your post are indicative of some sort of underlying mental issue that is beyond my scope and ability to address. You may need the services of a therapist, psychiatrist, etc. or whatever, but I just recommend you speak to someone about it with appropriate medical training.
I think you need to ensure you understand what's going on
There are lots of different family structures. Mother, father, child is what we'd typically call a nuclear family type setup and it's fine if that's what your life is. However, your life is not that. Your life includes 4 uncles that are part of your child's life on a daily basis.
My wife uses the term 'alloparent' for this situation and it can be helpful to think about things with this term. Alloparents are really anyone that serve in a parental role for children and it can include aunts and uncles, grandparents, friends, teachers, daycare workers, etc. Children learn from their parents and they also learn from their alloparents. And honestly, thank goodness for that because kids are a ton of work and it definitely takes a village to raise them.
Because of the diverse number of people involved in raising a child, it's pretty reasonable to expect that they'll all have their own style of parenting as well.
I am assuming that you and your wife, in general, have a style of parenting that you accept and enforce. However, given that your post indicates a lot of parenting is being handled by your wife and her brothers, then it seems likely that you are not as present. I don't mean this as an insult, but rather a matter of fact. Personally, I work a ton of hours to provide for my family, but that means I cannot be there as much as I want to be.
As a result of this absence, when you arrive and find that your brother-in-laws are shouting at your son you may not be aware that they've been trying to get him to do something for over an hour at that point. Indeed, it's very possible that when your son's uncle shouted, "No!" about taking him outside it could've been because your son refused to put on pants half an hour before you got there and the punishment for that was we're not going outside.
This seems doubly likely because when you interact with your son, a lot of his responses are variants on, "No." Might be phase, might be the flavor of the day.
It may be that you're unaware that in order to get your son to do what he needs to do, it's necessary to be very firm with him. Your post indicates that 2 of your brother-in-laws are very loving, but you don't indicate whether they get your son to do whatever he needs to do. Parents and alloparents can be loving, but that doesn't mean they aren't disciplinarians as well because pants need to be worn in Target and I don't want to have an argument about this in the middle of the electronics section.
I would recommend that you speak to your wife and ensure both of you are on the same page regarding what your child needs. This type of conversation needs to happen often because children's needs are always changing. At this time, I would not focus upon trying to alter the tone of her brothers, I suspect that she's irritated with you by the question because you're conveying ignorance to issues she's just spent all day dealing with.
Once you have that conversation with her, then you can attempt to figure out whether a conversation needs to occur with her brothers regarding whether their parenting matches what you and her aim for.