Ooh, I dunno loggie. Maybe get the father to take some parenting classes, get some anger management techniques, get the he to sit down and talk to him 1 on 1.
Or really, if at this early point you have recognized he doesn't actually have a parenting bone in his bone and isn't prepared to develop one, make some sort of decision about becoming a real lone parent. Instead of a lone parent who happens to be shacked up with a penis. Because all that does is perpetrate the cultural norms of 'oh, he's so useless wiv my babba, I have to do everything!' In gleeful tones.
It's insulting to all the real fathers out there, and sets a terrible precedent at this early point in his relationship with his child. If he isn't going to have a relationship with her, it's far better to break it off now, so that both man and child don't grow up believing that women do babies, and men do fuck all with their kids.
If he's an arse, kick him to the kerb. If he has a redeemable bone in his testosterone ridden body, get him to step up and accept he was an utter twat, and learn how to parent like a man. Not lose his rag like a toddler.
And any other women sucking their teeth and advising the op to do everything and let the be-penised one have a nice sleep are just as bad.
Either he steps up, or he ships out.
Only the op knows if he's redeemable or not.
But he doesn't get to be a parent in name only, and to sleep like a king under some load of bollocks like he can't cope. Time to learn how to cope.
Anyone that suggests this is a workable alternative is batshit crazy, and is perpetuating ridiculous stereotypes. And excusing this piss poor excuse of a man, when they should be saying 'oi, shape up, or fuck off'.