You're gonna have to basically be Kirk and dealing with the kobayashi maru.
So, get enough blackmail material or other leverage on the problem player or otherwise make a deal that is contingent on his good behavior to get something he wants so that he doesn't **** all over the game.
Because it sounds like that's the situation the DM is trying to engineer here. So you might want to address why even the DM hates the campaign.
Failing that, once the party looks like they're going to acquire the item... be the only person with pepto bismal.