The wording is not right because I'm tired, but you get the idea.

So, opponents put cards into exile instead of graves then you can play them from there?

Might be a bit stronger but you could word it as "Whenever an opponent discards a card, exile it. Return it to its owner's graveyard at the end of turn." and "Activation: Choose target face-up card in an opponent's exile. You may play that card as long as it stays exiled."