Background
My condolences on the loss of your mother-in-law, that is a very difficult situation. Something to note, everyone is grieving and may make even simple interactions more difficult (even if it has been months since the passing). It sounds like the eldest brother might feel like he needs to step up and try to fill the shoes of his parent. On top of that, there's a lot of change that comes with trying to combine families/households, that's always very difficult.
It seems like this issue stems from a bigger situation of trying to mix families, as this living situation does not sound temporary. It would be beneficial to plan and address this as a whole, as there are other issues as well (such as you feeling as though others aren't carrying their weight and making this a comfortable home for all). While it doesn't completely fit, there's a lot of good advice out there and support groups on how to blend families. While typically aimed for merging step families, there's still a lot of good stuff out there and just ignore the bits that don't apply. A simple example: https://www.helpguide.org/articles/parenting-family/step-parenting-blended-families.htm
I don't know about your specific relationship, but you really need to talk to your wife about this FIRST. She is your parenting partner who needs to be included, the literature on the benefits of parenting together is extensive and many relationship issues stem from when a parent feels as though they aren't being treated as a team player. If you want to keep the involvement minimal because she is stressed and grieving, you can simply say that you notice this situation and plan on doing xyz to remedy it if she has no objections.
What to say? Family dynamics can be tricky, some ideas:
If your wife holds more respect/authority over her brother than you, then this should be a conversation your wife has with him instead (it is common for siblings to respect other siblings authority first before their spouses).
It sounds like it might be easier to get the other siblings on board first, so you could try talking to them first and get them on the same parenting track. It's important to let EVERYONE know what you want them to do when he is naughty (not just what not to do).
However if you think he will respect you man to man more, then saying something simple offhand like SuperStew suggested would be good, especially since he is a proud man.
If you think something less bro and more heartfelt would be more effective, you could do something like: "I really love how you play with my son, it's great to see you two having fun. I want you two to have a great friendship and this new scolding stuff is getting in the way of that. I would really appreciate it if you could instead do xyz." You can ask that he help do something specific as part of your parenting plan, could ask him to defuse the situation and to let you know later for your wife and you to handle as a team later, etc. If he argues that he wants to continue to scold your son, you can explain the negative effects it has had and reiterate that you want your son and him to have a good relationship. If he does other things to parent your son, not just scolding, then I would leave out the bad guy bit and generalize more.
Another angle could be something like, “Hey I know things are really confusing and difficult right now with the passing of your mother and I just want you to know that you don’t need to step into a parent role for . I love how good you two play together and want you to have a good relationship, I know he can be naughty but I would like it if instead you did xzy.”
You could also pitch this as asking for his help and avoiding saying he’s doing anything wrong, “Hey I know you help take care of my son while I am work, and I would like your help with something as part of our parenting plan. When my son is naughty, can you do xyz so we are all consistent? This is a hard time for him and we’d really appreciate your help with this, you game?”
How to say it?
Think to some times you have had difficult conversations but were able to manage your anxiety enough to have the conversation. Remember the things you did well. It may be hard to remember a time you did well, ask a friend, they may be able to think of one. Breaking down sometimes you were successful may be the most helpful thing you can do to figure out a plan to have this conversation. I used to have a lot of anxiety with delicate conversations and while I was given a lot of tips by professionals that didn't work for me, the key was trying stuff out and identifying what did work for me.
Perhaps most importantly, you mentioned that this is a difficult conversation because you haven't interacted with him too much yet. Start by fixing that! What interactions are you comfortable with having with him? Find ways to do more of that. Maybe just small talk when you are home, go out for a beer, do something as a group together, etc.
Some stuff that worked for my conversational anxiety (even though I really didn't want to do it):
Thinking about what might appeal to the person I am talking to. Asking for help rather than telling someone what I wanted has been easier for me and usually appeals to the people I am talking to.
Rehearsing the conversation. Just getting over the physicality of talking was hard for me. Practicing it until the sound of my voice became normal and pronouncing the words felt natural.A lot of people suggest working with a partner, but that made it too hard for me. Just simply practicing it in the car by myself in the garage really helped me the most.
A lot of people say to take deep breaths, but this actually makes me feel anxious. Once I figured this out, focusing on taking normal breaths in and slightly slower exhales helped me a lot.
Remembering something positive that person feels towards me or a good interaction we had together and that they like me or like those I love.
You can always try writing something out that is has been carefully crafted and emailing it or leaving it as a letter in their room (so the proud brother can read in private and feel less on the spot and you don't physically have to have the talk).
You could also try having a sit down conversation with the adult members of the household about merging the families/households and this could be something that naturally comes up. You may feel less anxious of your topic isn't the main focus and if your wife is there to support you rather than one on one.
