A scenario where two people who don't like each other, go on a journey, and are STUCK with each other?

I have no idea about the parameters of your world, or the situation these individuals are in. If the world is still how it is today, I would say have the two of them in some kind of ground transport. Something like a jeep or whatever you like. It could be a broken down jeep but they're both in it. Maybe it was the only vehicle left. You could have it crash. Unexpected rock, soft sand where the tires sink and there's a sudden stop. Drivers knocks his head on the steering wheel because the air bags are old and don't work. Obviously they will travel together as it is necessary for survival. I could help if I had more of an idea about your settings. Shoot me an email at whiteleaf1217@gmail.com if you want to throw ideas back and forth until you figure it out, I get a kick out of thinking up events.