My current duvet has ties that can be used with the small loops at the corners of the comforter. I tie in the top corners, slide the cover down like a pillow case, tie in the bottom corners and shake. It works pretty well for us.
The kids beds have waterproof cover, fitted sheet, flat sheets, fleece blanket, and then a top comforter/quilt. DD has a light down one and DS has a quilt and a poly comforter he alternates between. I don't know that your kids' systems could be simplified within the preferences and constraints you have given.