After our kid my wife and I had these same fights.
Was the most stressful couple years ever. Eventually it calmed down.
Sounds like your wife has depression and staying home all day makes it worse. I felt the exact same way, I stayed home all day and worked evenings (from home) and started feeling like I was going crazy.
My wife is/was a bitch like how yours sounds. She was sort of always like that, but it got 10x worse after the pregnancy and even worse after the birth. And 4 years later it's still bad.
Hormonal changes are no joke. I don't have any advice. I'm sticking it out for the kid.
If you dont leave you need to put a end to fighting in front of the kid and neither of you should badmouth each other to the kid.