I was playing this morning and one of the control fields I created within another control field gave me more than 2k AP.
Does this give you more AP? Or might have I created 2 control fields with one link?

Inner fields don't give you more AP but it counts MU twice (which is good for your faction).
What happened to you is probably a link that create 2 fields at the same time (if you made the link between Homestead and Cutler bay in your picture, 2 fields were created). I like to create and destroy those kind of links :), more AP.