Let's say I have Darth Vader, Sith Lord with Maul's Lightsaber attached. Then, I play Pushing Slash to activate him. He rolls a 2 Melee with his die, and a +3 Melee with Maul's Lightsaber. Pushing Slash states that after you activate the character, you may resolve one of its character and upgrade dice. Since a modifier--in this case, the +2--modifies the amount of damage another die does, could I resolve the +3 with Vader's 2 when I play Pushing Slash, or could I only resolve his 2 Melee?

Note: I have been playing where you can only resolve the 2 Melee, since it only reads " one of its character or upgrade dice." I'm simply curious to see if I've been playing cards like this wrong.

Only the 2 melee. It says to resolve one of either your character or upgrade die. You have been playing it right.