When you are wielding a melee weapon in one hand and no other weapons, you gain a +2 bonus to damage rolls with that weapon…
When you wield a 2 handed weapon you are wielding a melee weapon in one hand and no other weapons" — because in the second hand you have the same weapon.
So in my view, if you allow players to hold shield in left hand and use Dueling, then using a versatile longsword or a two handed sword should be allowed too — it's the rules as written.
Is it rules as intended? Well, I think for shield-wielders there is Protection. Dueling is for duelists with the other hand free. (Or holding a rose, a candle, a bottle of rum — make it fun, not statistics!)