Pediatric Critical Care and Peds Pulmonary are separate fellowships, and to be honest, have significantly different focuses and career paths. Peds Pulm does a lot more CF/Asthma/BPD with a strong outpatient component. Peds CCM is entirely centered in the PICU and with the exception of some very rare circumstances, peds intensivists do zero outpatient clinic (although, it's likely that in the future, follow up clinics will be created similar to the manner in which Neonatologists have follow up 'high risk newborn' clinics).
There are some much older attendings spread about the country who are dual boarded in Peds CCM and Peds Pulm, but they are rare, and today's current climate would require a five year combined fellowship in the two. People who do the hiring would likely expect that if you completed those fellowships that you would have an interest in the care of children who are trach/ventilator dependent on long term home ventilation.
If you really prefer taking care of kids, then the question becomes do you prefer taking care of ICU problems (vents, sepsis, status epilepticus, fever and neutropenia in oncology patients, trauma, DKA, etc) or did you like the outpatient aspects of adult pulmonary?
Most people who go into fellowship from med/peds do one or the other, particularly for Critical Care. In other subspecialties, there is some precedent for combined fellowships, with the idea that you would then have specialized skills for managing the transition from pediatric subspecialty care to adult subspecialty care - ie the for the 18 y/o with Cystic Fibrosis, or the patient with congenital heart disease who has survived to adulthood. However getting these combined fellowships, even in these more logical fields, requires some negotiation with medical center and both departments which may not be as straightforward as one would hope (most departments of pediatrics and internal medicine don't have a history of working together - even med/peds programs are often the red headed stepchildren of both).
The final piece of the puzzle is getting a job and finding someone who will actually pay you to both if you manage to make it through the training pitfalls. Again, you would be an anomaly and there would be a fair amount of question of what to do with you. If you wanted to stay in academic medicine, then you'd likely be repeating the same battles you fought in fellowship. Private practice is an option, but there are far, far, far, far, far, far fewer private practice PICU's than there are adult ICU's, and there's even less collaboration between medicine and pediatrics.
