I'm not excusing anything. He shouted at her. He DIDN'T hit her. Stop tagging every man as an abuser. He scared her. THAT needs discussed in a calmer environment, This is not, for sure, a marriage that is beyond saving. And that is pretty much what you are all advocating.
Excusing is exactly what you are doing. He trapped her on the sofa so she couldn;t get away and shouted in her face she pushed him away and he raised his fist as if to hit her. He stopped THIS TIME. He has since tried to blame her for his aggression - she 'wanted him to punch her.'
This is how physical abuse starts - it never gets better it only gets worse. Normal people do not ever raise their fists to another person, particularly not someone who is holding a small baby. Next time he may not stop himself, next time he may go through with it, he may punch the OP and he may punch the baby if she happens to be in the way.
In your view she should wait for that to happen before taking any action.
All the signs are there of an aggressive abusive man. I know from experience it gets worse, each time a bit more threatening until you are too frightened to say anything or do anything that may make him kick off.
And you are saying 'aah he's sleep deprived, give him a break' - that is totally sickening and disgusting. It isn't OK to threaten violence, or to scare people - that is abusive behaviour. Shouting in someone's face is abusive behaviour. Your ignorance is astounding.
Contact the police OP. They will assess your level of risk far more effectively than an internet victim blamer, and they will give you advice and help. In my case once I had made a call they came out within hour, spent a long time talking to me and going through all his behaviour some of which I hadn;t even realised were classic signs of an abuser. They then had his behaviour on record and told me if I called they would come straight away having assessed me as at risk.