First off, no one trains in "ADULT EM." The ACGME residency training is Emergency Medicine, period. We aren't trained in how to manage poorly controlled, chronic hypertension, or how to diagnose MEN2 syndrome, or how to do a whipple. However, we are trained to manage all emergencies, regardless of the subspecialty. I hear lots of specialists bemoan how things are managed in the ED. That's everyone in medicine's favorite pastime - what else is new?
You're trying to speaking about a topic on which you sound poorly informed. If you're somewhere that even has Peds EM and Peds CC folks, you are, almost by definition, at a major academic center. The practice of Peds EM at a children's hospital that sees 50K children a year is vastly different than the practice of community emergency medicine that sees 25% peds - not only that, but the practice of medicine should be different. At the academic center, you have availability of all sub-specialists, you're seeing a patient population that consists of post-op congenital heart patients, advanced cancer patients, transplant recipients, kids with in-born errors of metabolism. When you work at a community shop, the kids you see have strep, a fever, a twisted ankle, etc. Sure, you see a septic kid once in a while, but the management of that at a community shop is very different. Parents of kids with transplants know to go to the academic center. You're job as a community EM doc is to 1) recognize that kid 2) perform any emergent, time-sensitive issues and 3) ship that kid as fast as humanly possible. If the kids not sick, your job is figuring out what needs to be done to keep that kid from dying between the time you see them and the time they can see their pediatrician. This is what EM residency does. It doesn't teach you to be a Peds EM attending - it teaches you how to manage a community ED where 25% of your patients are pediatric.
I am a senior resident at a major academic center - we rotate at a couple community hospital and I moonlight at another. I've seen medicine practiced differently and practiced differently depending on where I am, and that's OK. If the PICU attending doesn't approve of what I did before I ship the kid to the PICU, I don't really care - I care that the kid gets to the PICU safely. They have the benefit of being able to sit back and review the patient's history in it's entirety. I have 10 minutes to get the sick kid out safely - I have a guy who an LP, a lac that needs to be repaired, a tech handing me an EKG, notes to catch up on and a few charts in the rack; I need to recognize those beyond my ability and ship immediately - you learn to do that in a good EM training program.