Let me preface this by saying I am not a professional photographer, and I have modest computer skills, at least when it comes to networking.
What I want to do is this:
I have all my photos on an iMac desktop at home. I have a single Lightroom catalog with all the photos in it, including the RAW files. When I do an edit and get the photo the way I want it I export it to the hard drive as a jpeg for web publishing, etc.
I have just installed Creative Cloud on a MacBook Air which I will take with me on travels. This is so I can edit photos and publish them to my associated websites while on the road.
What is the best way for me to then put those photos, including the edits, onto my main home computer and into Lightroom catalog?
Once you are back home you can Export from the Air as a Catalog that includes the images and then Import From that catalog on your main desktop system.