How can I get an (iMovie-created) movie in the Videos app into iOS iMovie to edit it?
iMovie only supports the H.264 format, and will only load videos from two places:


Camera Roll
Synced iPhoto Library via iTunes (Photos Tab &rarr; Sync Photos from iPhoto &rarr; Include Videos)


As you've noticed, videos in your iTunes &rarr; Movies folder will only sync to the Videos app, and will not appear in iMovie.

The process is not at all convenient, but here's a video detailing how to convert a video to the right format on a Mac, and then get it into iMovie on an iPad: https://www.youtube.com/watch?v=oF8-sDmD_1Y.  He uses an app called StreamClip Video Converter to convert to H.264.  You might be able to get away with exporting that format from iMovie on your Mac instead.  iMovie is picky about the format though.  If you have trouble, try to reproduce the settings in the video exactly.