Leaving for work everyday while wife stays home, and I feel terrible.

TLDR: I feel terrible leaving for work everyday and leaving my wife with our fussy daughter. Is this normal? How can I help her more? Is my sleeping during the night selfish? It's about 4 or 5 hours of sleep on average. Full-time working dad's/partners of Reddit, what did u do? Am I sleeping too much? Do I feel guilty because I know I should still be doing my part at night?Our 2mo daughter is a handful, to day the least. We love her, but she's crazy. Lol. Crying restless nights (3-5 ur sleeps if we're lucky), won't let us put her down during the day, (sleeps all day in arms) and struggling to eat et every meal (exclusively bottle, bMilk and formula mix).It's been amazing. Seeing her bright big smile makes it all worth it!Anyway, my wife is obviously stressed, anxious, and exhausted, all with lack of any actual sleep since birth. We have no real support system that we can use. Her fam is small and busy, mine is small and ... An extreme last resort for my wife. (Not the issue here).I leave for work every day feeling absolutely terrible leaving my wife alone to deal with the fussy baby. I get home and understandably find everything in disarray, and I spend a good 1-2 hours just cleaning. Not to mention cooking and helping to prep for tomorrow (cleaning bottles, setting up formula, arranging diapers, etc)It's tiring for me, and so I try to get a night's rest for work the next day, but even then I feel guilty. My wife says to just sleep, she take care of the night feeds, changes, etc. To which I am grateful. She's an amazing mother and glorious wife. Selfless and loving.I try to do my part in holding the baby when I'm home. And give my wife a bit of time alone .... But theres so much to do she can't rest. She'll have to pump, clean, prep for tmrw, etc.Anyway, by the end of the night we're both exhausted, but I get to sleep. She gets restless sleep (wakes to every little sound, and will stay up literally watching the baby for hours, carrying her and rocking her back and forth), and continues the feeding cycle at night.Am I doing this all wrong? Should I be awake at nights too to help? I WANT to, but also (admittedly selfishly) need rest for work the next day.I'm just worried I'm doing this all wrong and being a weak partner. via /r/Parenting http://bit.ly/2GUWoL7