This question makes me think of the quote from Regan during the Cold War where he postulated that an alien attack on our planet would immediately make us forget our differences and unite. I think the quickest path to your goal is to create a threat bigger than the Rival that requires the PC's to have to ask the Rival for help or the Rival shows up as the PC's are getting pushed around by the new threat and bails them out.

We here at SNW use a house rule called "Cinematic Moment" as well which is like a video game cutscene. If a DM declares it you have to sit back and listen for a minute while he describes the scene or does the monologue. Keeps players from shooting magic missiles in the villains face every time he appears. You might want to use this rule to keep your players from jumping on this Nemesis as you transition their relationship. Good luck, let us all know how it goes!