My friend and I both play Barbarian and have ran into the same problem at the same time, when he handed one of his old swords down to me after he made a new one and suddenly both of our characters were using the wrong Main hands.
The problem is, that when dual-wielding, our characters will always use a specific weapon as off-hand weapon, no matter in which slot the weapons are equipped in and in which order they got equipped in.
For example, my character is using a Balrog Blade with an Oath Rune-Word, and no matter where I put it and what weapon I use in my other weapon slot, the Balrog Blade will always be used as the off-hand weapon for all damage calculation and all skills. Even the characters 3D model shows this. The Balrog Blade is always in the characters left hand. No matter in which slot I equip it. And no matter in which order I equip my weapons.
After some experimenting, my friend and I found out, that this seems to be a bug specifically with all types of swords that have BLADE in their type name.
It works correctly, with a Colossus SWORD.
But it is bugged with a Colossus BLADE.
It works with a Crystal SWORD.
It works with a Giant SWORD.
But it is bugged with a Balrog BLADE.
(Edit: I thought we also tested this with a Phase Blade, but apparently, we missed that one. Can someone please try and see if this is bugged with a Phase BLADE too?)
I would urge all of you to please try and see if you can replicate our findings. It would be interesting to see if this bug is actually limited to these specific Item Types, or if you can find any other combinations that contradict out findings!