Firstly, i've done PVG transit last year LX-SQ. No picking up bags etc, just had to go through immigration (using the transit desk). Interline agreements aside, is it all on one ticket?
That being said, travelling NRT-ICN-TPE-HKG-BKK-SIN with 2 young kids?!? Madness is the only word I can think that comes to mind.
goodo