Your mother sounds self-absorbed but your attitude about women who aren't "Independent" because they need their mother after having a baby, is a little naive I think. It was normal in human history for women to have the support of other women, especially their mothers, after having a child. Having a baby makes you vulnerable, physically, emotionally, even financially, and other women are the ones who have been through it. No man has been through the experience of having given birth to a child and all that entails. You are predicting that your husband will step up and be your support but it's possible he will find himself overwhelmed by the experience.
Newborn babies are different. Meeting a newborn baby is really, really special, and I can see why a grandmother would want to be there. After a few days they turn into "regular" babies, and they are still precious but there's a certain something to being there in those first days when they are looking around and everything they see is new to them. You will get most of that as the mother, but it would be nice for your mother to get a little of it too.
That said, newborn babies sleep a lot. After a couple months they "wake up" and interact more, start smiling, look chubby and cute, etc. So there will be lots of adorable moments your mother can share with the baby after the first month.
I think it's a little strange that your mother thinks it was fine for the baby to be separated from its own mother in NICU, but that what's traumatising for the baby is being away from its grandmother. There is something a little unnerving about that attitude. I don't think you are wrong to want to have some boundaries. Especially if she lives a 6 hour drive away, it would be easy for you to permit her to "pop around" to meet the baby for an overnight, and her end up being there for a week because, having brought some luggage, she effectively has possession of your spare bedroom. And if she is the overbearing type, that could be very stressful. You do hear about grandmothers who keep grabbing the baby from the mother and won't give it back, and you don't want to be in that situation.
But the idea that you need 3 weeks of uninterrupted time to bond as a nuclear family is somewhat overkill, in my opinion.