I would like to find a children's SF book I read in the 1980s. I don't recall the last length, but I know it had scattered illustrations.
A group of kids go over to the house of an inventor, probably related to one of them. The inventor was depicted with a white goatee; I remember his beard being described as "triangular.". He had built a teleportation device. I think it looked like a giant lightbulb, sitting on a waist-high table, with a pair of levers in front of it.
After some philosophical falderal about alternate realities, the device is activated. There's a crash, or flash, or something, but nobody seems to go anywhere. However, there are now two of each of them. The twin inventors decide that they must come from very similar planets. Both built machines, but only one worked, teleporting everyone to the site if the other world's (non-functional) device.
There is argument about which device worked and whose planet they are on. The last thing I remember, but I know it wasn't the end, was everyone going outside and seeing the sky was green.