If she didn't start sleeping those number of hours until after having the baby, this sounds like it could be postpartum depression. I'd recommend she gets evaluated by a psychiatrist to confirm, of course.
Poor kid is stuck in the middle. Doing my best for both of them, I really am, but I gravely underestimated how hard this would be. I thought years of being on call would prepare me, but it’s an entirely different kettle of fish.
Antidepressants are serious business. If you're actually just exhausted, it seems like you would be better off changing your environment rather than your brain chemistry. My wife has been on antidepressants since suffering from postpartum depression from our first child. Her current prescription seems to have her leveled out, but has also suppressed important aspects of her personality and perhaps even memory. This past year we've been in a rut where she refuses to even discuss changing anything because it's easier for her than confronting her underlying trauma.
For what it's worth, if you're fly-crawling-suicidal tired, it's better for you and your family to let your baby scream in their crib for an hour or two while you go sleep in a car. It isn't going to traumatize your baby, and might even be healthy for them to learn how to self-soothe. If you can afford it, it's also ok for you to occasionally take off a night and stay alone in a hotel, and let your wife take care of the baby. It would be more effective than antidepressants, assuming exhaustion is truly the root issue.
That will solve most of your health and mental problems.
Being a martyr getting no sleep and destroying your body and mind so your wife can sleep 12 hours isn't helping your wife or your kids. Not in the short term and 100% not in the long term.
You are going down a path that will result in major health and mental issues for yourself and at the end of the day, your wife and kids will hate you for what you allowed yourself to turn in to... a mean, unhealthy, unstable, fragile, and eventually dead husband.
