We both about lost it in the hospital due to sleep deprivation and being
overwhelmed with the *immensity* of it all with Child #1. We both agreed then that I needed my sleep to help out when she and the baby got home, and she would need her sleep (put baby in the nursery) to prepare for her return home.
Thereafter, neither was even a question. You (and the baby) staying in the room is just dumb, pointless, and (ultimately) counter-productive for all 3 of you. Good luck.