The Joker is too much of a badass NOT to show up in part 3. He was the architect of number 2 and as it was STATED VERY OBVIOUSLY. Joker and the Batman complete each other. Both are outcasts, both are psychotic (1 more than the other), and both fight for their ideals. I REALLY enjoyed that aspect of the movie, they need each other and the day they don't is the day they stop making batman.
The joker NEEDS to be recasted. The same as Heath? Of course not. Heath was a scary/nightmare/clown. His time in arkham could make him a more refined silly and equally intelligent clown that we all know and love. Batman grows up, he progresses his character so why shouldn't the Joker's character get a "new look?" It would differentiate both Jokers and allow yet another interpretation of him continue in the universe.
And by grown up I mean shorter, cleaner hair, and nicer suits.