Is it possible to use ffmpeg to move part of the video to another position and crop the video at the same time?
Basic syntax is

ffmpeg -i in -vf "split=2[pip][full];[pip]crop=W:H:X:Y[pip];[full][pip]overlay=W-w:H-h,crop=iw-M:ih:M:0" -c:a copy out


where W,H,X,Y are as per your diagram. M is the margin from the left edge which needs to be cropped out. Select M so that iw-M results in an even number.