Was child admitted?
I', not sure why you'd want to bill both, as the critical care fees are quite high, include many services, and are reimbursed quite well.
Our practice protocol would be to bill ONLY for the Critical Care charge.
In any case, I can't tell from your description ... was the child admitted?
If YES, and the PCP was the admitting physician who assumed overall care of the baby, then the PCP would probably only bill CPT 99293 (Initial inpatient pediatric critical care). This can only be billed once per day, but it is a pretty "all-inclusive" fee and is reimbursed quite well.
If the patient was only seen in the ER ... it would depend on the documentation. You would bill 99291-92 as appropriate based on time spent caring for the critically ill patient in the ER.
F Tessa Bartels, CPC-E/M