Parent of triplets on a throwaway account here. Some of this may come across as rude, sorry.
- You have one baby, you truly don't know the meaning of stress.
- Talk with and listen to other good parents at work/in your life.
- The What To Expect... books were gold for us as first-time (x3) parents.
- Your kid will be perfectly okay if they're on formula (but definitely give as much breast milk as you can).
- Alternate night-feeding duties between you and your wife. Then be glad you don't have two hands and three babies to feed by yourself on that shift.
- While doing all of this and the night shifts, I still had to work 40-50 hours a week at a job. I was mostly unproductive for 6 months.
- Man up and support your wife. All I hear is me, me, me. Your wife is under way more stress than you and her body is still recovering (physically/hormonally). Our situation was compounded by a serious episode of post-partum depression. Fortunately, we got through that intact.
- This time will be over quickly and some day you will actually look back and miss it.
> Last night, my wife was almost yelling at the baby because she won't drink the milk and it was really frustrating. This needs to change.
Try to be understanding of her stress and do anything you can to alleviate it.
> Our baby wakes up every 3 hours on average for milk and her mother is pumping milk.
She can pump during the day and put the milk in the fridge.
> Our own relationship (wife and I) seems shaky suddenly and she has started resenting me.
You need to communicate. You need to understand your wife is healing and under the stress of much more responsibility than you. Try not to take the resenting personally. Support her any way you can.
And yes, I learned all of this the hard way by making a lot of the above mistakes.