The paladin in my game frequently uses his backhand to "correct" the ranger/assassin/warlock. The table enjoys these social interactions, as part of their bromance. It mostly happens out of combat, but we do still roll damage for the slaps. Since the paladin is not the smartest of the bunch this could potentially backfire if he hurts his ally too much (or at the wrong time), especially since the ranger is now vulnerable to radiant damage (due to homebrew events).
According to How much damage does a punch deal?, by default:
An unarmed strike deals 1 + Strength modifier damage.
Improved Divine Smite (IDS)
By 11th level, whenever you hit a creature with a melee weapon, the creature takes an extra 1d8 radiant damage.
I read somewhere that an unarmed strike counts as a simple melee weapon and therefore allows you to add proficiency bonus to attack rolls if the (N)PC is proficient in simple melee weapons. But unfortunately I can't find the source for that statement. If this is true, it implies the IDS would trigger when hitting with unarmed strikes.
Research, with sources:
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons).
For example, an unarmed strike counts as a melee weapon attack, even though the attacker’s body isn’t considered a weapon.
Both accepted answers suggest that the slapping hand itself would not count as a weapon, and would therefore not trigger IDS, as the back of a hand is not a melee weapon. Although these answers hint towards my conclusion, they don't give a clear yes or no to my question.
Does Improved Divine Smite trigger when a paladin makes an unarmed strike?
In other words, is my current conclusion correct? Or am I misinterpreting the wording of the paladin feature?