Oh! Gotta love this sitcom! And Betty White as Rose Nylund is my favorite. Watching American comedies is a big challenge for the learner though. It's real hard if you don't live there so can't pick up on cultural differences and nuances. So my advice would be, don't go too far with sitcoms unless your English is damn good. :)
Back to your questions though. I think the clerk is jokingly saying that some can get busy talking while the next tornado is ruining their mobile home. This could be something like a trailer, a caravan. You should know that America is infamous for its tornadoes, right? And some people prefer living in mobile homes.
If something is on the back burner, it is temporarily not being dealt with, especially because it is not urgent or important. The clerk is playing on words meaning that some big pots (some desires) should always be kept on the back burner, i.e. suspended permanently. Basically he's telling Dorothy to never try a nudist camp (because her look is not appealing).
Dorothy is probably annoyed with the clerk because it's never good to date your close relatives like sisters, brothers, etc. "Don't you have a cousin you should be dating?" is a humorous, yet offensive way of her saying that.
Hope this helps!