You don't know she's being unreasonable or if he is. There's simply not enough information to determine that. Could go either way.

I hate to break it to you, but not all babies take naps or nap easily. Some of them it's WWIII every nap time to get them to go down. Some babies scream their heads off for months on end. While colicky phases typically hit around 4 months if they're going to, it's no guarantee. Sometimes they come out that way and don't shut up for a year. So don't count on colick ending after 6 to 8 months either. Some babies just never take to being separated or left alone in a room.

Maybe Mom had a traumatic delivery and needs more recuperative rest than what she's getting. Maybe Dad's got an easy job or one where he could take a nap at work more easily than she can at home with a newborn (like an EMT or a fireman, or an ER nurse). Maybe all this fuss is because he doesn't want to get up at night, not because he can't.

Or, maybe he has a job where he needs to be on point and she had a really easy birth but he just got a little snippy about the request and is making a mountain out of a molehill. Maybe she's fine with it but she's in the throes of some post partum depression and he's being all high handed about it so she's like, "my life is over!" In other words, she's more upset with how he asked than what he asked. Or he's just assuming she's upset and emotional because she's having wild hormone fluctuations.

Literally, anything could be going on here. We don't know. We're hearing it 3rd hand and there's a lot of info and nuance missing to be taking sides and talking smack about divorce and who's getting taken to the cleaners and who's crying about being a victim.