Most babies are born in hospitals and hospitals function best on routines. They’ll explain that “routinely we take your baby to the nursery for a bath and an exam and Dad can go along.” Tell them that this is your one and only special baby and that the “routine baby” must be next door. The baby’s not dirty and doesn’t need a bath. If they need to know what he weighs, the scale has wheels and his temp can be taken under his arm in your arms.
Babies born prematurely or with any problems or instability are a completely different issue and you’ll be happy you’ve chosen an OB you trust, a pediatrician attentive to your baby and a hospital which can handle the problems or prematurity.
But, most babies are born at or near term (37-41 weeks) and need no extra attention from the nursery and don’t need to be separated from their moms and dads. Talk to your doctors and the nursery about this before you go into labor. It’s a much tougher discussion at 6 or 7 centimeters dilation.
Vitamin K is a slightly controversial topic. I believe it should be given orally rather than by injection, but most doctors and other expert disagree and have good reasons for their position. Discuss this with your doctor and read a little about the topic.
Previously silver nitrate and now erythromycin or tetracycline is used in newborns’ eyes to prevent the transmission of gonorrhea and chlamydia. Research published in mainstream journals has repeatedly stated that choosing no eye care at all is a reasonable option. Again, most experts disagree, but the research is clear and I recommend no eye care at all for babies who have responsible parents, good prenatal care and pediatric follow up. I have a more extensive article on this subject here: Neonatal Eye Care
Rooming in and not sending your baby to the nursery at all is accepted practice in many if not most hospitals. Again, almost all of this advice is applicable to healthy full term babies only.
Leave the hospital as early as you can but secure good follow-up for the first few days of life. Either a three day doctor visit or, preferably, a home visit from a lactation consultant to make sure that breastfeeding goes well in the first days and weeks. Get the help you need.