Moviepy: how to do advanced composition between two clips (e.g. insert a movie inside a (possibly moving) green rectangle in another video)

Question

I am attempting to insert, with MoviePy, a video (dog.mp4) into another video's green screen, while resizing dog.mp4 to fit perfectly inside the green rectangle. It seems like this cannot be accomplished using the image_transform custom effect (doc), as it only allows for one input video. Any suggestions on how to approach this issue?