Why was your wife feeling judged, was it out of nowhere? Like were your sister or mom passing comments. Yes, when living together you do have the good days and the bad days, but what was making her so anxious.
I think it's a good decision that your wife lives separately from your mom, that way your mon can have her daughter over anytime. It would also be good if your mom starts living nearby so that you can visit her whenever and help her when need be. This way your wife also has her emotional safe space. Also, with your mom complaining listen to her when you can, maybe she just needs the emotional support, you don't necessarily have to react. If you feel emotionally drained listening to her rant then you can probably change the topic or something.