The New Two-Charge Smite
The 15 second window just makes it feel as though it'll make jungles needlessly fast in the jungle with things like Trailblazer (Purple Smite) as well as when people take Lane Smite, they'll never lose trades if they take Skirmisher's (Red Smite) because of the damage reduction and if they take Stalker's (Blue Smite) they'll be able to constantly slow harass their opponent with true damage. You can't tack it on to the summoner ability. It's going to be far too strong in that state.
What I suggest instead, is to implement a completely new smiting item (Yes, another one)
Harbinger's Hatchet Passive - Double-Tap: The user is able to hold two charges of smite, but can only smite Baron or Dragon once every 15 seconds. In addition, you will not gain additional benefits if you smite a large monster camp twice. (Maybe a debuff?)
Passive - Jungler: Blah blah blah
Make the background glow yellow, orange, or black. I do NOT want double-smite to put lanes in a worse place than they already are with the inability to fight back against things like that. If you do implement a double-smite, do it this way or don't do it at all.