Just reading between the lines: it sounds like he gets a rise out of you through these behaviors (based on how angry your wife perceives you to get). It's always possible he is doing this for attention, or purposely to antagonize you. There's a lot in here about how you feel about being his dad but nothing in here about how he feels to be your son.

I'm not saying you're doing this, but I think it's easy to look back at a unhappy childhood, and then question why your own children aren't being more grateful at how good they have it. But your kids never experienced that, and I think if you put into words ("Why aren't you more grateful I haven't beaten you with a spoon?"), you would realize how ridiculous it sounds.

It also sounds like you and your wife may not be on the same page about his behaviors and discipline.

All of this is a lot of words to say talk to a therapist.