Pediatric NPs?

Acute care is not the same as critical care. NP scope of practice is not defined by setting (absent a few states that have more stringent guidelines). An PNP-AC can practice in hospital settings, peds emergency or urgent care, specialty clinics, or combinations of the above. I would suggest reading this document which gives a much more through answer but basically:
https://www.pncb.org/sites/default/files/2017-02/NONPF_AC_PC_Statement.pdf

“The acute care CNP provides care for patients with unstable chronic, complex acute, and critical conditions. Both acute and primary care CNPs might treat patients with similar conditions, such as patients with diabetes and asthma; however, the severity and instability of presenting symptoms might help to define the needed provider at any given time.“

Unless one was also trained as a primary care PNP, they could not sit for the exam (nor could they sit for any other exam they are not trained and qualified for). There are some programs that include dual training for PNPs at both the acute and primary care specialties and one could complete a post-masters in another specialty but training in one specialty does not make one eligible for certification in another.