in our hospital, we always have 2 RN's in vag deliveries, and if there has been fetal distress or mec we also call RT in, just in case, and then if everything is OK, RT leaves. Then one RN cares for mom's recovery, vitals, fundal checks, etc, and the other cares for baby, assessment, meds, vitals, etc, until they are ready to be moved to their postpartum room. Then, one RN usually takes over both mom and babe.
If it is really hectic, we still have 2 RN's for delivery and for the first few minutes until we know that babe is stable, and just "warming up" and the OBT takes over for vitals on baby, while the RN recovers mom and keeps an eye on babe.
In C/S, only one of our RN's go, and RT ALWAYS goes, so there ARE two NRP certified personell there... the anesthetist is there to monitor mom, and circulator too, and then they go to recovery where the recovery room nurse cares for mom until transfer to our unit.