I don't think there is a "right" and "wrong" answer - it depends on what you are trying to do. Personally I have settled on the pattern of doing as much as I can in Character Animator (Ch) and avoid using the other programs because my laptop is not that powerful. I found After Effects (AE) too slow. So if I must use it, I do. Otherwise I try to use Ch.
I then export each scene as a separate movie file and stitch them together in Premier Pro where I add a bit of titling, sound effects that span scenes, etc. I have a 10 minute episode I am creating, which can take 4 hours to render on my laptop. So exporting one scene at a time allows me to edit and rerender an individual scene.
If you computer is faster, then you might find the AE and PR etc work great. Keyframing in AE is much better than in CH for example. But I put up with CH because its faster for me (less wait time). I only use AE for the tricky scenes.
But if you can create scenes completely in CH, then there is no need to use AE. If you can compose a single scene with your whole cartoon in CH with no need for PR, then there is nothing wrong doing that. I just found I needed PR to trim a few frames from the start of scenes due to puppets doing weird things at times when using draggers (the arms jump around a bit at the start sometimes). So I use PR because of a need.
Oh, to create one big scene from smaller ones, create a new empty scene, then drag the other individual scenes from the project panel into your new empty scene. Scenes can contain other scenes on the timeline. Its pretty easy to do, and i often do this as well for a quick preview (even though I later export each scene as a separate movie file and assemble it all in PR).
Thank you very much for the detailed answer!