Does the bonus damage from the Dueling fighting style apply when attacking with a shield as an improvised weapon, using the Tavern Brawler feat?
The scenario I am trying to work out is as follows... A character grapples the bad guy with his free hand and then knocks him prone. The following round, could he then use his shield as an improvised weapon (assuming he has the Tavern Brawler feat if that changes things) and still claim the bonus damage from Dueling (i.e. 1d4+2, rather than just straight 1d4)? While it's hardly broken for a DM to allow it, I'd rather know if it works with RAW.
The Dueling fighting style description is as follows:
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.
While a shield isn't a melee weapon in general; "An improvised weapon is, indeed, a weapon, but only the moment it's used as such." as per Jeremy Crawford's Twitter. Meaning at the moment of the attack, you are wielding a weapon in one hand in order to perform a melee weapon attack, but as per this post, it wouldn't be considered a melee weapon.