The ideas you've got make sense. If there is name calling from him to her and vice versa, it is an indication that she's feeding into his behavior, which naturally will turn into a power struggle. Respect is mutual and is earned. She may try to start by being the adult in her responses to him. Meaning- setting limits and following up with consequences. This would mean at times being able to ignore his negative behavior i.e name calling and remain firm. Of course, you'd be back her up if you're at home and the two of you should think of consequences for specific behaviors so both of you use the same ones and are on the same page about how he is to be parented/disciplined.
Democratic style of parenting works better than an Authoritarian one. This allows the child to learn that even if privilege is taken away, it can be earned back by displaying desirable behavior. There are reasons why a child misbehaves such as attention seeking (even negative attention vs no attention), power, revenge or because of feeling inadequate . Below I've included a link on that based on Adlerian Psychology and the STEP (systematic training for effective parenting)
He may have a need to belong especially if he feels that she in some way is taking your attention from him. The two of you may speak about that as what he tells you may not be something he tells her. There have to be activities within the home that foster a sense of belonging and pride such as him helping you and her with certain things, being in charge of age related responsibilities, receiving positive feedback/praise and encouragement which are essential to the STEP module.
Your wife would have to monitor her reaction to him and figure out why his behavior is causing her to act a certain way versus another. She would want to change what she's been doing because it had not been effective and try to apply positive parenting techniques and how she speaks to him. She would want to avoid power struggles. She is the adult and he is the child. The two of them are not on the same level and she has to set an example to him.
I will be off line now and will check your response later in the day and reply accordingly.