What possible reolution could there be? He's captured and in Arkham, Batman doesn't kill and The Joker isn't going to turn over a new leaf.
There's no way he can be used in any signifigant manner in the next Nolan film.
A significant part of the Batman mythos and indeed of the Nolan films has been escalation in response to Batman and the decline of the Mob in favor of the Freaks. Between the Joker, Dent, and Batman, the Mob is in shambles following TDK and the stage is set for the Freaks to take over in a big way.
Who better to orchestrate that change than the Joker, and where better to do so than from Arkham Asylum? Given his penchant for elaborate schemes (in spite of his claims otherwise), I wouldn't put it past him even to have wanted
to be locked up in Arkham in order to gain access to Gotham's most depraved individuals. Being in prison has never stopped Mob bosses from running the business, and I see no reason why the Joker can't do the same while essentially having control of the Mob and its assets himself and access to people as crazy as he is. He already employed lower-level Arkham crazies as his henchman in this movie, he'd just be moving up to a better class of nutjob.
Have Harley Quinn be a psychiatrist and former protege of Dr. Jonathan Crane's Scarecrow while he was working at Arkham, so she's already damaged goods. And then she meets Joker when he's incarcerated there and really goes over the top into evil. You could have Scarecrow in there helping Joker or have them briefly be rivals for dominance of Arkham and for Harley's twisted affection, ending with Joker brutally killing him and establishing himself as leader of the pack in the asylum.
How cool would it be to have a scene of Harley Quinn presiding over a "group counselling" session with much of the Rogue's Gallery, where instead of treatment they're actually plotting the downfall of Batman and running the criminal empire of Gotham? She could declare some of them cured in order to get them back on the street, with the Joker fomenting chaos from behind bars as their leader.
If Joker's appearance is so bothersome to you, he can always be seen from behind (doing the voice shouldn't be too hard), but I'd love to see another actor's take on the character, especially someone like Paul Betanny or James Franco.