The first such motive is that we have to deal with the fact that the kitchen and dining area are being expanded and it would be better for everyone concerned if minors were not in the middle of a construction zone. We could have the bog-standard Mike moaning "Aw, MAN!!!" because he doesn't get to shoot himself in the foot with a nail gun, the obligatory defensive gibberish from Elly about how she doesn't have to run ideas by her kids because she's their mother and they don't get to choose where they go and we could proceed from there.
The second rather obvious reason to get the kids out of town for a couple of weeks is to get Mike away from That Boy From THAT Neighbourhood. While she would go on to do this because she confuses a sternly policed slip of a girl whose parents distrust Michael with a calculating gold digger who wants to destroy the Patterson family because she never got over being a wall-flower who couldn't see that her growling about how horrible life was is why her dance card was empty, Elly didn't seem to see fit to punish Gordon for trying to make that spider go pop. We could have Mike incoherently defend his friend from his idiot mother while packing for camp and go on from their. We don't because Lynn has one constant motivation for putting space between John and Elly and their children: Trash Bag Johnny and Flapandhonk are a pair of fragile flowers who simply can't deal with their dull little offsprings and send them away to be brainwashed into thinking that they're dangerous rebels.