Sounds like you have a bully problem of your own.

You don't have a "Don't tell Mom" arrangement with your son yet? Not everything you say to your boy has to get back to mom. My dad was thrilled the few times I got picked on and then beat down a bully. My daughter stopped a bully from picking on someone else with just her words. The victim's mom called us to thank her. It's one of the times I've been the most proud of her. Don't let this special moment between a father and son pass unheralded! (It should be between parent and child, but your wife isn't on your side.)

Tell him in private. Mom doesn't have to know Mom also sounds like a bully herself. Her word is not the only word in your marriage

Geez. I'm surprised your kid stood up to a bully. Obviously not something he learned from you.

Also, standing up to a bully isn't being a thug...

My mother always got mad if i tried to stand up for myself. Teaching your kid to not stand up for themself only serves the parent by ideally making it easier to control them

No you aren't raising a thug, you'll be raising a victim who gets walked all over if you don't already give him a high five or nugde, or wink. The relationship you have with your son is your own to make.