I'm 45 and I found this very brave post absolutely apalling. If I was that DIL, I would have point-blank refused to engage with this MIL for the sake of my mental health which has to come first when looking after a newborn.
I think your wife's whole identity has been about being a mother but she's totally overextended herself and needs to back off now. There's nothing less attractive to a partner than their wife/husband acting like needy children. The apron strings have to get cut. It will be seen as enmeshment and control and definitely NOT appreciated.
I think your wife feels very threatened by this intelligent, capable, different, fresh, dynamic, thinking woman who MAKES YOUR SON HAPPY. She doesn't like it, therefore I'm worried she is literally going all out to remove your daughter in law. She doesn't like her because it's attacking her identity, her only identity.
It has to stop, boundaries need to be put in place, conversations need to be had so that your DIL doesn't leave with a newborn and never want to see your son again.
I really, really feel for her and I hope she is okay after a horrific year of sadness and a difficult birth.