Welcome to the forum
There is definitely some sort of inventory glitch in the game right now. Doppelgangers and missing items seem part of the symptoms with some people having both or one or neither! One of the symptoms I am constantly getting is duplicates and, like you mention if you drag out one of the duplicates often both have vanished from your game after going through a loading screen.
There doesn't seem to be any work-arounds presently but you just have to be super mindful of how you are using your sims personal inventory and the household inventory.
This link takes you to the Sims 4 Bug Reports. There are a few threads that sort of mention this glitch but nothing definitive that covers all aspects.
Also, it is totally worth your time to check that your mods are updated to the last game patch, and maybe even worth testing your game without them. Perhaps it is the mods causing the issues for you and that you in fact don't have the vanilla inventory glitch.