I know there are some kids at school who do this and TBH they seem to always be missing hats/shoes/homework! I kno sometimes with kids I have taught the homework thing is just an excuse but I think for this to work you need to be super organised.
My girlfriend does this sort of shared arrangement with her XH and she has ended up leaving sets of clothes etc at his house and having others at hers, her XH also won't do any washing for the boys so she gets all the dirty washing brought home too!! She has to remind the boys to bring all the gear they need home with them from their dad's.