When I had a newborn, and said newborn was premature and had disabilities, and I was super sleep deprived, and I had PPD (manifested more as anxiety), and was solely responsible for all income and infant care, and I was working in my own business, my boyfriend asked me to move with him to another city. I pondered it very briefly, and said no, primarily because in the current place I at least had some practical support from family members, and could afford my living space, whereas in the new city I would have increased expenses and reduced supports. I made a decision from a parenting point of view only. (A few years later I had a moment of kicking myself about that, because I was alone and lonely. I told myself, "Next time someone asks you to come live with him, you say yes." But that was only a moment. I stand by my decision to put my capacity to parent first.)
So, a few thoughts:
1. Even a person with all these circumstances can respond calmly and kindly.
2. However, a large part of the reason I could respond calmly despite all these variables was that I was not invested in that relationship. I think this is good news. i.e., Your wife may be panicking because she is invested in your guys' relationship, and wants a life with you. Okay, so throwing around the divorce word is not the ideal way to communicate that, but I still think her emotional response may actually give indication of investment/desire.
3. Post-baby is one of the most stressful times for a LOT of couples. Regardless of the gender of each parent, either or both will often feel shell-shocked, horrified at the thought of returning to work, exhausted, stressed, and scared -and experience a total re-evaluation of all things previously held dear. It's a wild time, emotionally, psychologically, physically, and logistically. If you want to stay married, I would make "stay married" your primary goal right now. Well, "keep child alive" and "stay married". No other new goals today. It's awesome that you do have additional options, but I would hold off on setting any of those as priorities right now.