Is it reasonable to tell family not to bring kids to visit in the hospital after delivery?

S • mama to a babygirl 💗 expecting baby #2 in May 💞

After I give birth to my daughter we will only allow select family and very few friends come visit the baby. I am really worried about germs and kids carry so many of them (I know there is a difference between good germs and bad germs, I am not a Lysol-on-everything-mom, but this is a newborn with no immune system we’re talking about here). I also know kids don’t wash their hands very well and they don’t understand that if you wash your hands and then cough into your palm then your hands are no longer clean. My cousin gave birth a few weeks ago and her 5 year old sister came to the hospital to see the baby, and she coughed right in the baby’s face. Of course she’s just a kid and didn’t really know any better, but I just feel I would be more comfortable not having small children there.

Is this unreasonable? I am not going to change my mind but I’m just wondering what everyone else thinks of this.