Hi, without really knowing you personally or academically, it's hard to formulate an opinion on what you should do. The previous poster made some very valid points; I know new grads who would take ANY job, hospital or otherwise. Even in the hospital, they would take ANY unit. Unless you have an "in" to a specific NICU, you need to realistically consider the fact that this will not be your starting point. And once in there, you need to ask yourself why you are doing this. As stated, it is an incredibly delicate environment. You ate blessed to have been part of a positive experience (not saying it was a cake walk for you and your child, but the fact that he is alive is a wonderful thing). So many of those babies do not survive, or do with many lifelong complications and struggles.
As a professor, I honestly say I am turned off by students who snub their noses at the other clinical units and specialties (yes, M/S is a specialty). I am not saying every nurse has to want a career in med surg (I did it for 2 years, then moved to Peds). I also love to hear what students true desires are. But what I'm trying to say to you is, of you do continue on, is advise you to at least pretend to have an open mind about your future.
As far as your calling and your desire: yes, you need more than that to make this happen. I feel like we live in a "reality show" mentality now. If someone says "I want this more than anyone here", they feel like they should get it. It takes tons of hard work. And you have to like what you do, and in nursing school, that means liking elderly, psych, critically ill adults, children (not neonates) women in labor, cardiac, respiratory, renal and oncology patients. In my school, our students never see a NICU patient. They see normal newborns, but that's usually it. And you have to pass those classes, even if you have no desire to be a psych or Peds nurse.
I can't tell you if you are doing the right thing. But you are going to have to make a lot of sacrifices, including time with your small children (I hope you have the support), whether you are in class on campus or online. You can't just show up to succeed.