This is annoying, I was playing around with dual weapons but it turns out that no matter what hand you have a weapon in, switching to it via hotkey puts it in your right hand. I have a heal hotkeyed to my left hand and two single hand weapons hotheyed. When I heal and then hit my weapon key the weapon just replaces what is in my right hand. Things work fine going from a two hander like bows, you can press the two hander key a second time and the dual weapons come back.

I haven't looked into this much, but I have noticed that if I hotkey a spell in my left hand, for instance, if I hit it once, it goes to my left hand, if I hit it again (with it still in my left hand) it double equips it. Maybe give that a try? Good luck.