I think those of you analysing the actual incident are making the mistake of not acknowledging the context of the incident.
Of course saying "go back to sleep" in a stern voice isn't in of itself abusive.
But this man already has a history of abuse. He's already used violence against the OP before this incident and he makes it very clear that he doesn't want to be asked to "help" parent his own child.
The context here, is that she usually doesn't ask him because he is "grumpy" about it. That to me sounds like minimising of eggshell-stepping - the reason some people are permanently "grumpy" about something, is so that they're not asked to do it. When adults do it about looking after their own children, combined with other abusive behaviours, it's recognised as an abusive behaviour.
One of the reasons emotional abuse is so much more difficult to identify and more pernicious than physical abuse, is because it's actually incredibly hard to spot it. This is a classic example: you give the verbal message that you're willing to "help" parent your own child and then every single time you're asked to do it you make clear that you are resentful and unwilling to do it. What this leads to, is the narrative that you are a willing co-parent while the reality is the opposite of the narrative - the other parent is afraid to ask for co-parenting and does the "eggshell treading" thing around that particular issue. But because of the narrative, it's her fault she doesn't ask for help, because the narrative helps to obscure the reality.
That's how emotional abuse works. And there is no physical abuse ever, without emotional abuse underpinning it. I really do think context is everything here and those of you only looking at the incident without acknowledging all the underlying dynamics, are making a mistake - probably with the best will in the world, but 1 in 4 women live with domestic violence and the lack of recognition of its dynamics, is one of the major reasons why. I think it's really important that we recognise it.