If the provider who takes an after-hours call is not the same provider in our practice who saw the patient in clinic, is that time able to be included in the total time of care?

Per the AAP, yes, so long as the time is spent on the same day, it is cumulative with the same physician and same physicians in the same group practice and the same specialty. How you bill it out (ie, under which physician) is an internal decision and nothing CPT addresses. Each physician should clearly document the total time spent.