@exoticfruits
The question is not 'is she responsible if not there', but whether she senses that this is how she might be treated. Because I sure as buggery think it is how mothers, especially SAHMs, are treated, and I never even suffer from it (just look up thread-if child is sensitive it is her sensitivity to blame).
Look, I've both stayed at home when an SAHP while my partner took the eldest away, and taken the eldest away. This is how I think the weekend might look:
Dad goes off with daughter. There are three adults who are friends in a child-friendly environment and the children entertain each other and have a great time. When they are asleep laughs, reminiscences and the odd drink are had by all adults. Everyone, including the daughter, is happy.
Mum stays at home with the breast-feeding baby. She talks to no other adult all weekend, perhaps indeed nobody since she has a pre-verbal child. She is physically knackered (I was just paranoid about the EBM running out), totally alone and unable to turn off in any way.
And on top of that she may sense that he is viewed as a bit of a hero (look up thread, it's all 'perfectly lovely' and 'really kind'). And he is certainly more likely to be be seen that way because a man and because it is his family. And he had all week for adult interactions and for a role other than as a parent, and she hasn't.
And so you have a really toxic mix where the parent who is suffering most is precisely the one who is seen as being treated exceptionally well, almost indulged by an OP who works so she can stay at home (interesting way of putting it, given parental care has been decided on she is also staying at home so he can be in employment)
What worries me most is that I can imagine many valid reasons why she is pissed off, and he can see none. And I'm a total emotional idiot.