Unable to deliver at hospital

My hospital would be unable to deliver my baby before 36 weeks due to not having a NICU. They ask that if I go into labor that I come there to get checked, if there’s an emergency they could do my C-section, but my baby would be separated from me and flown to a hospital about 90 minutes away. One nurse told me that she shouldn’t share the info, but she drove the 90 minutes to deliver her baby when he came early, and didn’t get checked at the local hospital first in order to not have to be separated after birth.

I’m only four days away from 36 weeks but I have a Type A personality and like things planned out. Does anyone know if smaller hospitals are flexible if it’s a day or two away from 36 weeks, or if it’s a strict policy thing?

Thank you!