I don't think this is caused by the mods since they don't mess that extensively with the game, and to clarify by inventory do you mean the "menu" instead? the one where you see the character portraits and the menu tabs(items, skills, settings, etc).
And if those are the mods you run then it wouldn't make sense for those to affect the inventory.
As for your last question, unfortunately you can't remove mods mid-game, you have to close the game, remove a mod then start the game again.
The game itself can also be pretty buggy at times, but if you got some other bugs/potential bugs let me know!