I don't know of any (free) MPEG-4 editor, as the MPEG-4 codec and its variants (Divx, Xvid, H263/4, ...) are not meant for editing, they don't save every frame, which is important for exact frame editing.
I would do it the following way.
Use MPEG Streamclip to convert the MPEG-4 encoded .mp4 file (most probably H264) to a DV file (which uses the DV codec and uses 226MB/min), then import that into iMovie and re-arrange like you want, and then export again, either as H264 encoded .mp4 or as QuickTime and use that .mov in MPEG Streamclip to transcode it again into an .mp4 file.
OR
You could download the Adobe Premiere trial and see if that is able to import the .mp4 file, then use Premiere to re-arrange and export it as you like.
That might save you some encoding processes. The trial is fully working for 30 days by the way.