I didn't have any expectations when I clicked but I thought the video was great! I would agree that most of the motivic connections are probably intentional. The composers of the time were, after all, expert craftsmen, and motivic connections or basing a big work on one basic motif were often used to create a large qauntity of varied material while keeping a sense of unity. That descending fourth being everywhere is not just a coincidence. The only thing I think one can argue about regarding this is just details about exactly where the rising sixth and descending fourth are hidden in some instances. EDIT: Regarding motivic connections - Beethoven was big on those and learned it from Haydn, and Schumann would have studied and admired Beethoven's work.
Good work! I agree with your assertion, these kinds of motivic and structural interrelations are often central to the conception of unified bodies of work like the Kinderszenen. You should look at the late Brahms piano pieces if you haven't already. They're so tightly composed that I'm sure there are some interconnections between pieces.
Thank you! I adore the late Brahms piano pieces - any in particular you had in mind?