You sound like a lovely caring husband OP.
You need to sit your wife down (during the quietest time of the day), and have a talk with your wife. Mention that she looks like she is sad and angry and you really would like to help her feel better - is there anything you can do to help? Tell her you love her and you want to support her and your children.
I also had 3 under 4 and it was hell on earth when my third child was born. I also suffered from postnatal depression and my husband travelled to work late and came home tired and grumpy and didn't help much. I became angry, resentful and really sad.
She is probably exhausted from having a small baby (probably lack of sleep) and having two other bouncy children full of energy in the day. Does she get to sleep extra when she has bad nights? Do you regularly help with chores around the house without being asked? Help cook sometimes? Take all the children out for trips? Accept that with 3 under 4 keeping the house tidy is a major battle that might not be won for years to come…
Does your wife have other support - her family / friends? Maybe you could offer to take the children one day during the weekend so she could socialise with others without the anxiety of running after the children.
It is important that your wife gets as much ‘free time’ as you do during days off (where she isn’t doing housework!). Imagine you were working 24/7 without any time off to relax - it is not feasible, both night and day shifts without a rest can send any person crazy.
I hope your wife feels better soon.