Are you the favorite or something? The youngest? Just because she has been a certain way for so long and other people allow her to talk to them that way doesn't make it right. It sounds like your mother needs to be put in her place. Once you are married your wife is the number 1 woman in your life. Your mom probably continues to do whatever because she feels like you never really say anything so it's ok. It has to come from YOU and you have to be firm. You can't say " *insert wifes name* was upset by what you said" or "My wife doesn't like the way you..." You have to use words like I, we, us, etc because y'all are a union, a team and it should offend/upset you that your mother treats you wife that way or hurts her.
If you don't insert youself into it, or put it all on your wife even while talking to your mom it won't matter. She will just brush it off as your wife doesn't like her and you really don't care. Children live the home to go be with their spouse. Your wife should have to stand up to YOUR mother. You can stand of for your wife and be respectful.
It is not even the wife pickering. In OP he says she is passive in public. The only bikering/fight they had was when it came to a boiling point. It sounds like the mother is constantly saying something to the wife then she is asking him to handle his mom. If he sits them down like they are both causing problems that will blow up in his face. If I was the wife I would be mad if I'm sat down to have a talk like I am causing issues when I only said something at my breaking point because my husband won't say anything. She would feel even more alone in the situation and her mother would get validation like she isn't the problem it's the wife or they are both the problem. He needs to talk to his mother.
I'm the second oldest. My wife asked me last night am I scared of my mom. I'm like what kinda question is that. NO, I just don't want her mad at me or my wife. But I've talked to her ad nasueum about this. My wife has been trying to get me to move to the west coast, but I wanna move back east but moving isn't the full answer. I just need to talk to moms but I know she will then say I'm siding with my wife but I am. That's MY wife. Hopefully she'll get it this time. I get to work today and got these white folks looking at me crazy wondering who was that screaming in the background when I got the call to come to moms house...smh, This can't happen again.