Set reasonable adult boundaries.
next he will shout at you
Full stop right here. Reasonable adults don't get a free pass yell at each other. We have the ability to use words to communicate with one another. If he's upset about something he can use his words to explain why, and you can discuss if there was desired or undesired offense.
So you set the boundary: "Dad, I love you, but I'm simply not willing to be yelled at by you anymore. It hurts me deeply. However, I'm absolutely willing to hear you out if I've upset you. I hope this goes both ways. These are signs of mutual respect. So going forward, if we're having a discussion and you start yelling at me, I'm going to remove myself from the situation, and when you're ready to engage again without yelling, I'll be there to listen to you. If we're on the phone, I'm simply going to hang up. If we're in person, I'm just going to leave. I don't want this to be the way we operate, but until we can communicate without yelling, it has to be this way."
and then give you the cold shoulder.
So when he's doing this use communications/plans that self-fulfill, meaning the communications/plans require no more action on your part after you've sent them. Example:
Don't use:
"Would you like to get lunch together tomorrow?" - Cold shouldering by him means you have to wait for his answer to act. He has power over you and your attention.
Instead use:
"I'm having lunch near X tomorrow. I'd be happy if you joined me. Let me know by 5pm today if you're interested in joining me tomorrow for lunch." - This way if he doesn't respond, his inaction is the response. You require nothing of him to go on with your plans. His actions or in-actions simply don't affect you.
It doesn't mean you don't have to keep working with him to grow up and be a functioning communicative adult. Its entirely possible he's too immature to have the kind of relationship you really want with him, but understand the alternative to healthy boundaries is you and your wife getting hurt by him on a regular basis. With healthy boundaries the negatives will shift from "hurt from him" to "disappointment in him".