I quite agree with this post and those of other posters such a @the7Vabo - especially the comments about mummy boy posts and “ manning up” by telling his mum to get lost, he has a “new” family now ( sentiments you see a lot on MN). It is in no sense a normal or natural thing that a man grows up to devour his mother like some sort of brutal insect when she ceases to be of use to him and spits her at the feet of his wife as some kind of demonstration of manly devotion. When I’ve seen men do this, far from being a manly gesture, it has usually been the capitulation of a spineless, hen-pecked DH who lacks the emotional wherewithal to grapple with the situation and is being puppeteered by a wife who often manifests many of the traits she accuses the MIL of .
Relationships do take work and a degree of tolerance in the true sense ( not in the currently popular sense of a one-sided concept). Mothers and wives are not in competition and all this rhetoric about mothers who see the wife as competition is something that makes me think those espousing it need to look quite hard at themselves. Mothers naturally want continued involvement in their children’s lives and the suggestion that it is somehow narcissistic or controlling or envious or prurient is a symptom of the emotional sickness and self-centredness of our generation more than anything else.
I commend the OP for trying to balance his loyalties to the people who are meaningful in his life. It can be difficult, but the current trend for simply casting people off is not always, ( and not often), the answer ( actual abuse is obviously a different scenario). I can see both the mil and his wife have put him in a difficult position.
The op gave a helpful list of the issues. The bit about the breast-feeding was annoying I’m sure; but honestly, people have to get over these things. If she were still trying and failing to breastfeed then yes, I could see it might impact the wife’s Mh. But I presume she has either stopped or resolved it (?), so to pretend to op that being a woman and enduring childbirth is such a destabilising process that it somehow continues to do so is manipulating you as a male op.
The bit about the brother is actually none of the wife’s businesses and is clearly adduced as extraneous character assassination. The brother could be entirely the problem - or just part of the problem, because in fact that’s usually the reality in these types of family dynamics. None of us are perfect.
The bit about the rant in the car? She had an opinion about something that was ( understandably) disappointing to her. People express emotion. Move on. That’s family life.
The bullets about the child are, I can see, a very valid concern for your wife. However, rather than banishing mil from the kingdom, as it were, all that this calls for is not leaving the child alone with her again. End of.
And as another thought, people do get hurt by things like being left by a spouse, they can and do develop coping mechanisms that can include drawing emotional support from others, including their children. Obviously, where op himself finds this an issue he is entitled, and should, gently explain it. But again, it’s a case of relationships being a work in progress and not some kind of justification to bin his mother like faulty merchandise or old fish past it’s use by date. It’s that latter approach to relationships that has led society to the confused and broken point it is at. As @Whatado has pointed out, we have simply swung on a pendulum from one kind of assault on boundaries and MH to another.