I let my wife know that nobody believes her.
Why don't you want people to believe your wife?
She doesn't think she's physically abusive, but occasionally she pushes me around and yells at me...
Telling your wife that no one believes her when she says she is not abusive is not enough. Staying with her and not leaving is wrong. You need to get out of the toxic, abusive relationship with your wife.
I promise I'll keep my cool, or I'll leave.
I think you should just leave now, this relationship is not healthy.