You mention that she’s suffering from post-natal depression and as such it’s going to be very, very hard for her to tell the difference between anger at you, anger at her predicament and anger at herself. Being depressed does horrible things to your self-esteem which can escalate any underlying ill-feeling.
My wife is in a fragile place, she seems to have deferred all the blame on me for actions last year since she was diagnosed as suffering post natal depression. I think they call this transference. I dont believe I’ve done anything wrong, I would do all the same actions the same if it was repeated. I had to make some on the fly decisions regarding her mental health care, making sure the kids were ok, some were like the choice between a bullet in the brain or a glass of poison. Either way I was screwed.
You sound like you’ve done everything in your power to be responsible and look out for the interests of your children. You’re also able to hold back and try to remain objective.
There has to be a way of finding a safe environment for your partner to talk about her feelings away from the marital home. Once she’s properly allowed herself to analyse the sources of her anger then it may well be that she’s prepared to give relationship counselling a go?
FWIW, please give yourself a massive pat on the back fella, because it’s more than I’d be capable of doing in a similar situation.